Question: Show that if A and B are two n x n matrices that both have the same diagonalizing matrix X. then AB = BA.

Show that if A and B are two n x n matrices that both have the same diagonalizing matrix X. then AB = BA.

Step by Step Solution

★★★★★

3.38 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If A XD 1 X 1 and B XD 2 X 1 whe... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

949-M-L-A-E (811).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(a) Give an example to show that if A and B are symmetric n n matrices, then AB need not be symmetric. (b) Prove that if A and B are symmetric n n matrices, then AB is symmetric if and only if AB =...

Q:

Show that if A and B are similar, then det A = det B.

Q:

Show that if a and b are positive integers, then ab = gcd(a, b) lcm(a, b).

Q:

(i) Consider the vectors x, y, z in R and the expression xx (yxz) +z x (xxy) where denotes the vector product. How can this expression be simplified? (ii) Let A, B, C be n x n matrices over C. Let...

Q:

1. [-/1 Points] DETAILS 0/100 Submissions Used 1 2 0 0 Solve the equation for X , given that A = and B = 3 4 -1 1 2(A + 2B) = 3X X = Need Help? Read It Submit Answer2. [-/1 Points] DETAILS 0/100...

Q:

a Give an example to show that if A and B are symmetric n x n matrices then AB need not be symmetric 02 OA 2 3 B 1 4 which is not symmetric OA 3 2 t B 10 23 OA 20 13 20 OA A OA B B but AB but AB but...

Q:

(8 marks in total) (a) (4 marks) Let A and B be two n X n matrices such that A2 = 1, B2 = I and (AB) = I, where I is the nXn identity matrix. Prove that, in this case, AB = BA. (b) (4 marks) Give a...

Q:

HHelp me to solve the questions as attached below. 3. Consider an economy with A consumers and B rms. Each consumer is endowed with one unit of time and one piece of capital. A representative...

Q:

14. Let A and B be two n x n matrices such that AB' = 0. Is B'A necessarily equal to zero? Show that tr (B'A) = 0.

Q:

Question 4 (15 p) Assume that national income, Y, is exogenously set at one fixed level (full employment) in both the short-run and in the long-run, and that the exchange rate is floating. Assume...

Q:

A charge Q is transferred from an initially uncharged plastic ball to an identical ball 12cm away. The force of attraction is then 17mN. How many electrons were transferred from one ball to the other?

Q:

A decrease in earned capital for a non-owner transaction must accompany a decrease in cash when using cash basis accounting. o True o False

Q:

Which one of the following statements correctly applies to term insurance? Multiple Chofce The premiums remain constant. The policy builds cash value. Protection is for a specified period of time. It...

Q:

3. U.S. government price supports for milk led to an unceasing surplus of milk. In an effort to reduce the surplus about a decade ago, Congress offered to pay dairy farmers to slaughter cows. Use two...

Q:

Sketch u and its image under each given matrix transformation f. F: R2 R2 defined by 2 0 0 2L>

Q:

Sketch u and its image under each given matrix transformation f. F: R2 R2 defined by 001

Q:

Let f be the matrix transformation defined in Example 5. Find and sketch the image of the rectangle with vertices (0, 0), (1, 0), (1, l), and (0, 1) for h = 2 and k = 3.

Q:

j Alicia (age 27) is a single, full-time college student. She earns $13,200 from a part- time job and has taxable interest income of $1,450. Her itemized deductions are $845. Calculate Alicias...

Q:

The balance sheet for Ferguson Corp. is shown here in market value terms. There are 7,000 shares of stock outstanding. Instead of a dividend of $1.80 per share, the company has announced a share...

Q:

Question 4 Which of the following is not one of the three empirically observed facts related to the yield curve? Approximately half of the time the yield curve will slope up and half of the time it...