1. Let R2,² be the vector space of 2 × 2 matrices with entries in R.[a b]If A='then the trace of A is defined by trace(A) = a + d.Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB)defines an inner product on R2,2

Answered: Image /qna-images/answer/03e74ee0-414c-4b1c-8051-1d8a80fe97a3.jpg

1. Let R2,² be the vector space of 2 × 2 matrices with entries in R. a If A = then the trace of A is defined by trace(A) = a + d. C Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB) defines an inner product on R2,2.

1. Let R2,² be the vector space of 2 × 2 matrices with entries in R. a If A = then the trace of A is defined by trace(A) = a + d. C Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB) defines an inner product on R2,2.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 76E

See similar textbooks

Related questions

Q: How many elements does the vector space V over the field F={0, 1} have, if its dimension is dimV=8?…

A: The number of elements in a finite vector space can be calculated using the…

Q: Find the area of the surface generated by revolving the given curve about the x-axis. 4. x x=3y, 1 ≤…

A: The curve is :

Q: 2. a. Use Ptolemy's known chords from the reading (or from videos) and the half-angle chord identity…

A: Detailed answer shown belowExplanation:Certainly, I can help you with this problem which asks you to…

Q: If an electrician works hours a day at a job at $16 per hour, how much does he make working for 5…

A: To calculate the electrician's earnings, need to multiply the number of hours worked per day by the…

Q: Let Hspan {(-3,-1,-2), (17, -1, 10), (-5, 0, -3)}. A basis for the subspace HCR³ is { vector

Q: Find the instantaneous rate of change in the amount in the account at the time the amount is equal…

A: Given that an investment of $10,000 earns interest at an annual rate of 6.7%…

Q: Find a formula for the optimal cost. Hint: consider the cases when n is even and then the cases when…

A: Please go through the below answerExplanation:

Q: 3. (error) For what values of x can you use sin x ≈ x- with an error less than 5 × 10-4?

A: The aim is to find the value of "x" so that it is used The expression of

Q: Consider F and C below. F(x, y) = (1 + xy)exy i + x²exy j C: r(t) = cos(t) + 3 sin(t)j, osts (a)…

Q: A country has two states, state A with a population of 37,044, and state B with a population of…

A: Hamiltons methodPopulation of first/seats of first= population of second/seats of second Here…

Q: In the space R^4, the sets are given: B:={(4,1,5,2),(0,1,2,1),(2,1,0,5),(0,−1,5,−8)}…

Q: Nitin

A: Basis are (1,0,1) and (0,1,2)Explanation:

Q: How many different bit strings of length 7 with two 1's and five O's are there?

A: Sure, here's a step-by-step approach to solving the problem of finding the number of different bit…

Q: Arrange the given steps in the correct order to prove that 12+3+...+ Rank the options below. Assume…

A: Step-1: For n = 1, the left hand side of the theorem is 1/(1.2) = 1/2 and the right hand side =…

Q: 2X2 matrix with eigenvalues A₁ =-1.2, A2 = 1 with corresponding eigenvectors Consider the difference…

Q: 5-8 Find the area of the surface generated by revolving the curve about the y-axis. given 6. xy³, 0…

A: 6. Given, a curve Limits of integration: It is required to find the area of the surface generated by…

Q: The price-demand equation for hamburgers at Yaster's Burgers is x+395 p = 3,088, where p is the…

A: Yaster's determines that a hamburger costs roughly $3.91 to maximize revenue. Explanation:To…

Q: Find the supremum, infimum, maximim and mimimum (if they exist) for the following set (a) S₁ = {Q: 0…

Q: 9. e2y dx+2(xe²y - y)dy = 0

Q: This problem involves Pascal's Triangle. a. List the entries C(7, 0), C(7, 1), ..., C(7, 7) of the…

A: a) C(7,0)= 1 ; C(7,1)=7;C(7,2)=21 ;C(7,3)=35; C(7,4)=35; C(7,5)=21C(7,6)=7; C(7,7)=1 B) (a+b)7=…

Q: The best one can say, without actually solving the differential equation, x(x²+x-72)y"+9(x-2)y' +…

Q: Find the annual rate of simple interest that over 5 years accrues the same interest as (4) = 3% p.a.…

A: The answer is in the explanation.Explanation:Let ( P ) be the principal amount, then the interest…

Q: .19. Evaluate the series: S(x) = Σakxk, k=0 where (a) ak = 1,

Q: You go to the a local coffee shop with 6 of your friends to study. At this coffee shop they have a…

A: There are 153 gumballs in the machine. Out of them, 25 gumballs are sparkly. So, there are (153 -…

Q: Evaluate the following "curly" surface integrals (V x F). ds. (a) F(x, y, z) = yi – xj + zx³y²k and…

Q: Solve using augmented matrix methods -4x¹-5x²=-3 -8x¹-10x²=1

A: The objective of the question is to solve the system of linear equations using the augmented matrix…

Q: Let -4 3 17 A 4 4 20 4 -1 -11 Observe that the third column of A is -2 times the first column plus 3…

A: Answer is given below Explanation:Step 1:Step 2: Step 3: Step 4:

Q: Acav1: Linear Programming (Minimization) A chicken farmer uses a mixture of chicken feeds, Chicken's…

A: Let me show the given data in a tabulated form, Grams per unitMixtureChicken's BestChicken's…

Q: Miss Valdoz offered you a job which should be completed within 50 days. At present, you have xxx…

A: Miss Valdoz offered you a job which should be completed within 50 days.Let at present there are 100…

Q: A linear operator Lcan be used as short hand notation for an n-order linear differential equation.…

A: The objective of the question is to identify the incorrect expression of the given linear…

Q: Use your graphing utility to enter each side of the equation separately under y₁ and y2. Then use…

A: Y1 = 2x+2(x-7)Y2 = 3x-6

Q: Find the solution of the difference equation Yn+24yn+1+3yn = 2.3" with initial conditions yo = 2, y₁…

Q: work out the problems below refering to the sets:

A: H ⊆ C: False.Ø ∈ E: False.F ∪ D: F ∪ D = {1, 3, 5, 7, 9, 11}Cˉ: Cˉ = {1, 3, 5, 7, 9, 11, 13, 14}D…

Q: let x and g be elements of a group G. show that x and gxg-1 have the same order. now prove that xy…

A: Hence, proved.Explanation:Step 1:To prove that x and gxg-1 have the same order for any elements x…

Q: Use gaussian elimination to find the complete solution to the following system of equations or show…

A: The objective of this question is to solve the system of linear equations using Gaussian…

Q: For each of the following series, tell whether or not you can apply the 3-condition test (i.e. the…

A: Dear Student, As per our guidelines we can answer only first three subqustions. So kindly resubmit…

Q: Could you please help me?

A: The example of the set and their relation which is Symmetry , Transitive but not reflexive A=1,2,3…

Q: Find and solve the dual problem.

A: The answer is attached.Explanation:Step 1:

Q: Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and…

A: Given, A statement : A postage of cents can be formed using only cent stamps and cent stamps.It…

Q: Exercise 5 (10pts) Demands on a first aid facility in a certain location occur according to a…

A: The objective of the question is to find the probability that two demands occur in the first two…

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d) are subspaces .

Q: Q4.) F(s) L' = 45+93 252+85+40 } 45+9 252 = = 2 = +85+40 =2 2 L" { -1 L+ تو 2/2-1 -2t ? (pat し S+…

A: Here we use the sum and product by scale of Laplace transformation.

Q: x(t) = Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where A = = [12 -12]…

A: The answer is given belowExplanation:Step 1: Given x(t+1)=Ax(t) , where A=[−912−12−9] Step 2:Step…

Q: Solve using augmented matrix methods 5x¹-x²=6 15x¹-3x²=-18

A: The objective of the question is to solve the system of linear equations using the augmented matrix…

Q: Math 152 Week 12 Workshop Problems 4/1/24 Write up your solutions to each of these problems on a…

Q: Find the domain and solve. 10.6√x ≤2.6√x-8

Q: You may have observed that the Lagrange interpolating p(x) always goes to ±∞ when x → ±∞. This may…

Q: Please help me out

A: Equivalence Classes: The set S is divided into equivalence classes by ~, which is an equivalence…

Q: Suppose an economy has four sectors: Mining, Lumber, Energy, and Transportation. Mining sells 15% of…

A: First calculate the transition Matrix then find equilibrium.

Q: 5. Consider the inner product on P2(R) defined by (p,q) = * p(x)q(x)e¯dr. Construct an orthonormal…

Question

1. Let R2,² be the vector space of 2 × 2 matrices with entries in R.
[a b]
If A
=
'
then the trace of A is defined by trace(A) = a + d.
Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB)
defines an inner product on R2,2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

Step 2: Proof

Step 3: Proof

Step 4: Proof

Solution

Step by step

Solved in 5 steps with 4 images

SEE SOLUTION Check out a sample Q&A here