Question: Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = PAP is

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = PAP is the diagonal form of A. Prove that AK = PB*P-1, where k is a positive integer. Use the result above to find the indicated power of A. A = -11 -18 6 10 , 46 46 = 1

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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

Students Have Also Explored These Related Mathematics Questions!

Find a matrix P such that P AP orthogonally diagonalizes A. Verify that P AP gives the proper diagonal form. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a...

Are the two matrices similar? If so, find a matrix P such that B = P-PAP. (If not possible, enter IMPOSSIBLE.) 30 0 10 0 A = 0 20 B = 0 3 0 0 01 0 0 2. P =Let A be a diagonalizable n x n matrix and...

Need help with this problem, please show work. Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P AP is the diagonal form of A. Prove that AK = PB*P ],...

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B P AP is the diagonal form of A Prove that Ak PBkp 1 where k is a positive integer Use the result above to...

need answer asap 2. (4 pts) Let A and B be n x n matrices, and let P be an invertible n x n matrix. Show that if B = P'AP, then det(B) = det(A). (You may not simply state that the determinant is a...

Problem 1. Let A be an invertible n X n matrix. If A is diagonalizable, prove that A1 is diagonalizable. Problem 2. Let A be a 2 X 2 matrix with exactly one real eigenvalue A, and assume A has...

43. Let A be an n x n matrix. Suppose that there exists an invertible matrix P such that P-AP = D, where D is a diagonal matrix. Consider the following statements. (i) A = P D (P1)2 (ii) A2P-DP Which...

7. Let A and B be n x n matrices such that A + B is invertible. Then, show that: A(A + B) B = B(A + B) 'A. 8. Let A be a 3 x 3 matrix satisfying A OON =ei+e2, A 0 0 N = ei + (where ei, e2, es, are...

The purpose of this set of exercises is to explore a relationship between two matrix factorizations the LU factorization and the QR factorization The first example illustrates a QR factorization....

In SWMI on S : 1 . Write a matrix equation that determines the loop currents from Figure \"l 1. Solve the system for the loop currents. (10 points) In 2. The following statements are either true in...

To the right are the outcomes that are possible when a couple has three children. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the...

The Screamin' Eagles Company makes wheels and wings for ground transport vehicles and drones. In addition to the key manufacturing departments, Screamin' Eagles needs two key support services,...

FIN 3 7 0 - 1 0 0 9 / Which of the following is an example of a capital market instrument? Banker's acceptances. US . Treasury bill Common equity Commerdat paper:

Irene is saving for a new car she hopes to purchase either four or six years from now. Irene invests $17,000 in a growth stock that does not pay dividends and expects a 6 percent annual before tax...