let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. what is the dimension of h
Answers
let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. The dimension of h will be 0 ≤ h ≤ 3
If m be the vector space , a subset h ⊆ m is a subspace of m if the ten axioms (L₁ , L₂ , L₃ , . . . . L₁₀) of m are satisfied on h but it suffices only two axioms to hold on h for h that are axioms of closure of h under two linear operations : the sum of vectors and their multiplication by scalars in the field F.
Let m is a vector space over a field F, a subset h which is closed under the two linear operation of m : the vector addition and multiplication of vector by scalar .
L₁ (∀x , y ∈m) , x+ y∈ m ---------(1)
L₂ (∀λ ∈ F) ( ∀ x∈ m ) λx ∈m -------(2)
A subset h⊆ m which satisfy (1) and (2) is a subspace of v
Dimension of Vector space and a subspace :
According to linear algebra theorem,
The number of vectors in all the basis if finitely generated vector space m is the same. This number is just the dimension of subspace m : dim m .
If m is spanned then here, dim m = 3
h ⊆ subs m <===> dim h < dim m
If h is subspace of m and dim m = 3 then,
dim h = h with 0≤ h ≤3
If h is zero, the dimension of improper subspace , h = {0}
If dim h = dim m = 3 the h = m since any basis A of h is a basis of m too and conversely,
Hence , any vector m of all 3×3 matrices and h be its subspace , the dim h will be 0 ≤ h ≤ 3
To know more about Vector space here
https://brainly.com/question/13058822
#SPJ4
Related Questions
WILL GIVE BRAINLIEST!! The yearly population of a city with a 3% yearly growth rate and an initial population of 30,000 can be modeled by the following function where x is time, in years, from 2015.
f(x) = 30,000(1.03)x
The mathematical domain of this function is all real numbers, and its range is all y-values greater than zero.
Which statements describe how the reasonable domain and range compare to the mathematical ones? Check all that apply.
The reasonable domain has a minimum value.
The reasonable domain does not include zero.
The reasonable range has a minimum value of 30,000.
The reasonable range includes zero.
The reasonable range has an implied, but unknown, maximum value.
Answers
1, 3, 5
The reasonable domain has a minimum value.
The reasonable range has a minimum value of 30,000.
The reasonable range has an implied, but unknown, maximum value.
Step-by-step explanation:
1. Years cannot be anything below 0.
2. The domain includes 0 because the answer can be the initial value.
3. 30,000 is the initial value and is the minimum solution.
4. The range has a minimal of 30,000.
5. Logically, we know city populations cant be numbers like a billion but we prove that mathematically.
Answer:
1. The reasonable domain has a minimum value.
3.The reasonable range has a minimum value of 30,000.
5.The reasonable range has an implied, but unknown, maximum value.
Step-by-step explanation:
Find the midpoint between the following points:
(7.-7) & (3, 1)
Answers
Answer:
5,-3
Step-by-step explanation:
use the formula
substitute the number
and get the answer
Answer:
(x1+x2)/2,(y1+y2)/2
Step-by-step explanation:
use this formula
answer will come for sure
7=x1
-7=y1
3=x2
1=y2
PLEASE HELP ME WITH THIS QUESTION. 15 POINTS
Answers
Answer:b
Step-by-step explanation:
Answer: B). y=5x-6
Step-by-step explanation:
A is just the x-intercept
C is a parabola
D would just eventually equal to the x-intercept
Through deductive reasoning, we get B.
Solve the system by substitution . 5x- y =21 x=2y -3
Answers
Answer:
(5,4)
Step-by-step explanation:
To solve a system of equations by substitution, you need to solve one of the equations for one variable (either x or y). In this case, we can solve the second equation for x: x=2y-3. Then substitute this expression into the first equation and solve for y: 5(2y-3)-y=21. Solving for y gives us y=4. Substitute this value back into the second equation and solve for x: x=2(4)-3=5. Therefore, the solution is (5,4).
yw;)
Use your newly gained natural deduction skills to solve the following problems. In each problem, the arrow symbol means the same thing as the horseshoe symbol in the preceding chapter.1).1. F ∨ (D → T)2. ~F3. D/T2).1. P → (G → T)2. Q → (T → E)3. P4. Q/G → E3).1.~X → [~X → (Y → X)]2.~X /~Y4).1.K → (L → M)2.M ∨K3.~M /~L5).1. ~S→D2. ~S v (~D→K)3.~D/K
Answers
1. F v (D → T)
2. V F
3. D
∴ T
4. D → T (Disjunctive syllogism 1,2)
5. T ( Modus Ponens 3,4)
2. P → (cu → T)
2. Q → (T → E)
3. P
4. Q
∴ Cu → E
5. Cu → T (modus ponens 1,3)
6. T → E ( modus ponens 2,4)
7. Cu → E (Hypothetical syllogism 5,6)
3. 1. ~ X → [~X → (y → X)]
2. ~ X
∴ ~ y
3. ~X → (y → X) (modus ponens 1,2)
4. y → X ( modus ponens 2,3)
5. ~ y ( modus tollens 2,4)
4. 1. k → (L→m)
2. m v k
3. ~m
∴ ~L
4. K (disjunctive syllogism 2,3)
5. L → m (modus ponens 1,4)
6. ~ L (modus tollens 3,5)
5. 1. ~S → D
2. ~S v (~D→K)
3. ~ D
∴ K
4. ~(~S) (Modulas tollens 1,3)
5. S ( Double nojection 4)
6. ~D→K (Disjunctive syllogism 2,5)
7. K (Modus ponenes 3,6)
Hence we get the required answer.
Learn more about Natural deduction skills here:
brainly.com/question/7284582
#SPJ4
What is the solution to this system?
-- 3x + 5y - 4z = 10
2 x – 5y + z = 0
- 3x + 5y – 2z = -2
y =
Answers
Answer:
x= -8, y= -6/5, z= -6
Step-by-step explanation:
that is the answer
let f (n) be the function from the set of integers to the set of integers such that f (n) = n2 1. what are the domain, codomain, and range of this function
Answers
The domain and codomain of the function f(n) = n^2 + 1 are both the set of integers. The range of the function is all positive integers (including zero).
To find the domain, codomain, and range of the function f(n) = n^2 + 1:
1. Domain: The domain is the set of all possible input values for the function. In this case, since the function is defined for "the set of integers," the domain is the set of all integers.
2. Codomain: The codomain is the set of all possible output values for the function. In this case, the function is defined as f(n) = n^2 + 1, where n is an integer. Therefore, the codomain is also the set of integers.
3. Range: The range is the set of all actual output values that the function produces for the given inputs. To find the range, we can substitute various integer values for n and observe the corresponding outputs. Since the function is defined as f(n) = n^2 + 1, the smallest possible output value is 1 (when n = 0), and there is no upper limit for the output. Hence, the range is all positive integers (including zero).
Learn more About domain from the given link
https://brainly.com/question/30096754
#SPJ11
Tyson has a $50 gift card to use at a store. He does not have any additional money to spend at the store. Tyson will purchase a belt that costs $8 and x
number of shirts that cost $15 each. The function f(x) = 42 - 15x models the balance on the gift card after Tyson makes the purchases. What is the mo
appropriate domain of the function?
(A) all integer values of
B
all positive integer values of x
©
0 x< 2 where x is an integer
D
0<x<3 where x is an integer
First
Back Pause I
Next
Review I
Answers
0 ≤ x < 2, where x is an integer. Option C
The appropriate domain for the function f(x) = 42 - 15x in the given context can be determined by considering the constraints of the problem.
Tyson has a $50 gift card, and he wants to purchase a belt that costs $8 and x number of shirts that cost $15 each. The function f(x) represents the balance on the gift card after Tyson makes the purchases.
The number of shirts Tyson can purchase depends on the remaining balance on the gift card. Since each shirt costs $15, the maximum number of shirts he can buy is limited by the amount of money left on the gift card.
If we subtract the cost of the belt ($8) and the cost of x shirts ($15x) from the initial balance ($50), we should get a non-negative result, indicating that Tyson has enough money on the gift card to make the purchases.
Therefore, we can set up the inequality:
50 - 8 - 15x ≥ 0
Simplifying, we have:
42 - 15x ≥ 0
Now, we can solve for x:
-15x ≥ -42
Dividing by -15 (remembering to flip the inequality sign), we get:
x ≤ 42/15
x ≤ 2.8
Since x represents the number of shirts Tyson can buy, it should be a whole number. Therefore, the appropriate domain for the function f(x) is:
0 ≤ x ≤ 2, where x is an integer.
Option C.
For more such questions on integer visit:
https://brainly.com/question/929808
#SPJ8
What are all the values that a correlation r can possibly take?A. 0 ≤ r ≤ 1B. r ≥0C. -1 ≤ r ≤ 1D. None of the above.
Answers
The values that a correlation r can possibly take are -1 ≤ r ≤ 1. Thus, option C is correct as per the correlation relation.
Correlation is a statistical measurement that describes the extent to which two variables are linearly related to each other in positive and negative directions. The correlation coefficient is denoted by r.
The value of correlation r can range from -1 to 1. Here,
-1 indicates: a perfect negative correlation
0 indicates: no linear correlation
1 indicates: a perfect positive correlation
Therefore, we can conclude that the values that a correlation r can possibly take are between -1 ≤ r ≤ 1.
To learn more about correlation
https://brainly.com/question/30504806
#SPJ4
Factorise this pleasee
x2 + 4x -45
Answers
Answer:
(x - 5)(x + 9)
Step-by-step explanation:
1. MONDAY (5/18): Which of the following functions matches the graph to the right
a) f(x) = -⅙(x+3)²+6
b) f(x)=-⅙(x-3)²+6
c) f(x) = -6 (x+3)² +6
d) f(x) = -6 (x-3)² + 6
Answers
Answer:
a.) f(x) = -⅙(x+3)²+6
Step-by-step explanation:
The maximum value, our vertex, is at point (-3,6).
We can insert this value into the vertex form of a quadratic function and then solve for a as follows...
\(4.5 = a(0 +3)^2 +6\\4.5=a(9)+6\\-1.5 = 9a \\-.17=a\\a = -1/6\)
a equals -1/6... We can input this into the original equation we used...
f(x) = -1/6(x+3)^2+6
Good luck on the bellwork ;)
What is the slope of the line that passes through the points (-5, 6) and (-9, -6)
Answers
The slope of the line that passes through the points (-5, 6) and (-9, -6) is 3
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Let the given points as shown:
(x1,y1)= (-5, 6) and (x2,y2)= (-9, -6)
Slope = m = (y2-y1) /( x2-x1)
= (-6-6) /(-9-(-5))
= -12/-4
= 3
So, the slope of the line that passes through the points (-5, 6) and (-9, -6) is 3
To learn more about the slope from the given link
https://brainly.com/question/16949303
#SPJ1
Aslam and akram invested rs 27000 and rs 30000 to start a business . if they earned a profit of rs 66500 at the end of the year , find the profit of each one
Answers
The profit of Aslam is Rs. 31,474.50 and the profit of Akram is Rs. 35,025.50.
To find the profit of each person, we can use the concept of ratios.
First, let's find the total investment made by both Aslam and Akram:
Total investment = Aslam's investment + Akram's investment
Total investment = 27000 + 30000 = 57000
Next, let's calculate the ratio of Aslam's investment to the total investment:
Aslam's ratio = Aslam's investment / Total investment
Aslam's ratio = 27000 / 57000 = 0.4737
Similarly, let's calculate the ratio of Akram's investment to the total investment:
Akram's ratio = Akram's investment / Total investment
Akram's ratio = 30000 / 57000 = 0.5263
Now, we can find the profit of each person using their respective ratios:
Profit of Aslam = Aslam's ratio * Total profit
Profit of Aslam = 0.4737 * 66500 = 31474.5
Profit of Akram = Akram's ratio * Total profit
Profit of Akram = 0.5263 * 66500 = 35025.5
Therefore, the profit of Aslam is Rs. 31,474.50 and the profit of Akram is Rs. 35,025.50.
To know more about the investment visit:
https://brainly.com/question/29547577
#SPJ11
Which of the following describes the idea of the Laffer Curve as it is expressed mathematically?
The ratios show the relationship between the federal income tax rates and revenue
To analyze how economic policies may affect growth and stability
Aggregate supply increases when production costs decrease.
reduce the government's role in the economy
Answers
The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.
The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.
Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.
To know more about mathematically visit:-
https://brainly.com/question/27235369
#SPJ11
Two ice cream shops in the mall sell sundaes. Let x equal the number of scoops of ice cream. Larry's Ice Cream Shop's price is represented by the expression 1.2x + 1. Ice Cream World's price is represented by the expression 0.4(0.3x + 1) . Which statement is true?
Choose the correct answer below.
A.
The two shops charge the same price for a 3-scoop sundae.
B.
The two shops charge the same price for a 2-scoop sundae.
C.
The two shops never charge the same price for sundaes with the same number of scoops.
D.
The two shops always charge the same price for sundaes with the same number of scoops.
Answers
Answer:
the answer is D.
Step-by-step explanation:
this is because if you distribute 0.4 times 0.3 you get 0.12.
then you are left with 0.12+1 which means both shops charge the same price.
Q2( K=3,C=2) Compare and contrast work and power concepts with the help of the Venn diagram. It could include characteristics, examples and formulae etc.
Answers
Work and power are both important concepts in physics that relate to the application of force and the rate at which work is done. While they are interconnected, there are distinct differences between the two.
Work is defined as the transfer of energy that occurs when a force is applied to move an object over a distance. Power, on the other hand, refers to the rate at which work is done or energy is transferred.
Work and power can be compared and contrasted using a Venn diagram to illustrate their similarities and differences. In the overlapping region, we can highlight the characteristics that are common to both concepts. For example, both work and power involve the application of force and the transfer of energy. They are both measured in the same units (joules for work and watts for power) and are fundamental concepts in physics.
In the separate circles, we can outline the unique characteristics of each concept. For work, we can include the formula W = Fd, where W represents work, F is the force applied, and d is the distance over which the force is applied. Work can be positive when the force is in the same direction as the displacement, or negative when the force opposes the displacement. Examples of work include lifting an object, pushing a car, or climbing stairs.
For power, we can include the formula P = W/t, where P represents power, W is the work done, and t is the time taken to do the work. Power is a measure of how quickly work is done or energy is transferred. Examples of power include a light bulb producing light, a car engine generating horsepower, or a person running up a flight of stairs quickly.
By comparing and contrasting work and power through a Venn diagram, we can visualize their similarities and differences, highlighting the interconnected nature of these concepts in physics.
learn more about power concepts here:
brainly.com/question/30286015
#SPJ11
What number is in the exact middle of -3 and 1.5?
Answers
please help!
Solve this system of linear equations using linear combination/elimination.
Madeline has 19 coins in her backpack. Some are nickels and some are quarters. The total value of the coins is $2.15. How many nickels and quarters does she have?
Answers
Answer:
8 quaters 3 nickels
Step-by-step explanation:
21-7x/x+3/x^2-3x/2x+3
Answers
The given expression is\((21 - 7x) / (x + 3) / (x^2 - 3x) / (2x + 3)\). To simplify the expression, we need to apply the rules of fraction division and simplify each fraction individually.
To simplify the given expression, we start by dividing the fractions. Division of fractions is performed by multiplying the first fraction by the reciprocal of the second fraction.
The expression can be rewritten as\((21 - 7x) / (x + 3) * (2x + 3) / (x^2 - 3x).\)Next, we can simplify each fraction separately.
In the numerator, we can multiply out the terms: \((21 - 7x) * (2x + 3) = 42x + 63 - 14x^2 - 21x.\)
In the denominator, we can factor out an \(x: x^2 - 3x = x(x - 3).\)
Putting it all together, the simplified expression becomes \((42x + 63 - 14x^2 - 21x) / [(x + 3) * x(x - 3)].\\\)
Further simplification may be possible depending on specific factors and terms present in the expression, but without additional information or specific values for x, we cannot simplify the expression any further.
Learn more about rules of fraction division here:
https://brainly.com/question/12382709
#SPJ11
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
Answers
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
Read more about area here:https://brainly.com/question/27440983
#SPJ1
HELP PLEASE HURRY!!
Find (2.25 x 10^30)(4.41 x
10^4) using a calculator.
Write what your calculator
displayed and explain what
it means in scientific
notation.
Answers
Answer:
9.9225 E 34.
E = exponent
= 9.9225 x 10^34
Step-by-step explanation:
after paying 5.12 salad , kamauri has 27.10
Answers
The amount of money that Kamauri has at first will be 32.22.
How to calculate the cost?From the information, it was stated that after paying 5.12 for salad, Kamauri has 27.10.
Based on the information given, the total amount of money that he had at first will be the addition of the cost of salad and the change left.
This will be illustrated as:
= 5.12 + 27.10
= 32.22
The amount is 32.22.
Learn more about money on:
brainly.com/question/24373500
#SPJ1
After paying 5.12 for salad, Kamauri has 27.10. What was the total amount of money that he had at first?
What is an equation of the line that passes through the points ( -6, -3) and
(-8, -4)?
Answers
Answer:
y = 1/2x.
Step-by-step explanation:
THe slope of the line = (y2-y1)/(x2-x1)
= (-4-(-3))/(-8-(-6))
= -1/-2
= 1/2.
y - y1 = m)x - x1)
y - (-3) = 1/2(x - (-6))
y + 3 = 1/2(x + 6)
y = 1/2x + 3 - 3
y = 1/2x Answer.
If each shelf can hold at most 20 books, what is the least number of shelves needed to store the 175 books?
Answers
Answer- 9 shelves
In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.
HOPE THIS HELPS & GOOD LUCK!
Use the factor theorem to determine if the given binomial is a factor of f f(x)=x^(4)-9x^(3)+5x^(2)+5x-2 (a) x-1 (b) x+1
Answers
Answer: f(-2)=0; yes, the binomial is a factor of the polynomial.
f(-2)≠0; the binomial is not a factor of the polynomi f(2)=0; yes, the binomial is a factor of the polynomial.
f(2)≠0; the binomial is not a factor of the polynomial.
Step-by-step explanation:
Written as the product of its prime factors, 2250=2x3²x5³. Two integers, A and B, can be written as products of prime factors. A=2xpxq¹ B=2xp² xq² The lowest common multiple (LCM) of A and B is 2250. Write down the values of p, q and r.
Answers
The values of p, q, and r are p = 2, q = 5, and r = 3, respectively.
Given that the lowest common multiple (LCM) of A and B is 2250, and the prime factorization of A is A = 2 × p × q¹, and the prime factorization of B is B = 2 × p² × q², we can compare the prime factorizations to determine the values of p, q, and r.
From the prime factorization of 2250 (2 × 3² × 5³), we can observe the following:
The prime factor 2 appears in both A and B.
The prime factor 3 appears in A.
The prime factor 5 appears in A.
Comparing this with the prime factorizations of A and B, we can deduce the following:
The prime factor p appears in both A and B, as it is present in the common factors 2 × p.
The prime factor q appears in both A and B, as it is present in the common factors q¹ × q² = q³.
From the above analysis, we can conclude:
p = 2
q = 5
r = 3.
For similar question on lowest common multiple.
https://brainly.com/question/16054958
#SPJ8
Consider the proof.
Given: Segment AB is parallel to line DE.
Prove:StartFraction A D Over D C EndFraction = StartFraction B E Over E C EndFraction
Triangle A B C is cut by line D E. Line D E goes through side A C and side B C. Lines A B and D E are parallel. Angle B A C is 1, angle A B C is 2, angle E D C is 3, and angle D E C is 4.
A table showing statements and reasons for the proof is shown.
What is the missing statement in Step 5?
AC = BC
StartFraction A C Over D C EndFraction = StartFraction B C Over E C EndFraction
AD = BE
StartFraction A D Over D C EndFraction = StartFraction B E Over E C EndFraction
Answers
The missing statement in Step 5 include the following: B. AC/DC = BC/EC.
What are the properties of similar triangles?In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the angle, angle (AA) similarity theorem, we can logically deduce the following congruent triangles:
ΔABC ≅ ΔDEC ⇒ Step 4
By the definition of similar triangles, we can logically deduce the following proportional and corresponding side lengths:
AC/DC = BC/EC ⇒ Step 5
Read more on triangles here: https://brainly.com/question/11763540
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
2 (3)^3 + 5
And explain how you got it
Answers
Answer:
59
Step-by-step explanation:
3^3=27
2x27=54
27+54+5=59
Answer:
2 times 3 i 6 o 3 plus 5 equal 8
Step-by-step explanation:
beca you supoed to multiply ad divide
Which equation models this situation?
The sum of 24 and a number is 40.
2 of 12 QUESTIONS
24- x = 40
24+ 40 = x
40 + x = 24
24+ x = 40
SUBMIT
Add
Answers
Answer:
24+x=40
Hope this helped
Answer:
hes right look up there
Step-by-step explanation:
hes right :) only for a p e x
the number defects per part from an aging machine is shown below. number of defects (x) per part 0 1 2 3 4 5 probability p(x) 0.15 0.20 0.30 0.10 0.20 0.05 what is the mean of the data?
Answers
The mean of the following data is 0.1800
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.acc to our question-
100C5 * .05^5 *.95^95 ~ 18.00%hence,The mean of the following data is 0.1800
learn more about mean click here:
https://brainly.com/question/1136789
#SPJ4