Question: Let p be an invertible n n matrix. If A is any n n matrix, write Tp(A) = P-1AP. Verify that: (a) Tp

Let p be an invertible n × n matrix. If A is any n × n matrix, write Tp(A) = P-1AP.
Verify that:
(a) Tp (I) = I
(b)TP(AB) = TP(A)Tp(B)
(c) Tp(A + B) = Tp(A) + Tp(B)
(d) Tp(rA) = rTp(A)
(e) Tp(Ak) = [Tp(A)]k for k ≥ 1
(f) If A is invertible, Tp(A-l) = [Tp(A)]-l.
(g) If Q is invertible, TQ[Tp(A)] = TPQ(A).

Step by Step Solution

★★★★★

3.29 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

b T P AT P... View full answer

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)

950-M-L-A-L-S (6466).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let A be an invertible n n matrix. Show that the eigenvalues of A-1 are precisely the numbers 1/, where is an eigenvalue of A.

If A1, A2, , Ak, is an infinite sequence of n Ã n matrices, then the sequence is said to converge to the n Ã n matrix , A if the entries in the ith row and jth column of the sequence...

Let P be an orthogonal matrix. (a) Give 2 2 examples of P such that det P = 1 and det P = -1. (b) If P is n n and det P (-1)n, show that I - P has no inverse.

7, DUE Friday, March 10th, 2017 Hand in Part A and Part B as two separate assignments. Include the following information in the top left corner of every assignment: your full name, instructor's last...

Hi i need help with the problems highlighted and circled in red, its only linear algebra 176 CHAPTER 2 Matrices and Linear Transformations 4. Give the domain and codomain of the matrix transforma- In...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

Consider the following. 2 1 U 0 1 3 A = 0 2 D r p = 0 4 0 4 2 4 1 2 2 (a) Verify that A is diagonalizable by computing P'lAP. l-1 l l0 l l0 l Vim): o -2 0 : Jlii X (b) Use the result of part (a) and...

Story plot: tall, square, symmetric. For each technique, give the relevant matrix equations to obtain the solution x, and point out the properties of the matrices involved. Highlight one potential...

Your program will be a simulation of a trip of goats (sample), stored in a vector (recommended) or a data structure of your choice. INFO'S THAT CAN HELP FOR THE QUESTION We'll use a for loop to...

Why is it difficult to assess the effectiveness of discretionary cost centers?

"Exhal Energy Company (EEC) sells packaged, fresh herbs to health food stores. The company has several departments; however, we are going to focus on the last processing department, Packaging. The...

What factors most influence the effective output rate of a flow process?

Why are public goods not produced in sufficient quantities by private markets?

Find the characteristic equation of the given symmetric matrix, and then by inspection determine the dimensions of the eigenspaces. a. b. c. 2 2 4400 4400

Use the result in Exercise 17 of Section 7.1 to prove Theorem 7.3.2a for 2 2 symmetric.

Does there exist a 3 Ã 3 symmetric matrix with eigenvalues Î»1 = -1, Î»2 = 3, Î»3 = 7 and corresponding eigenvectors If so, find such a matrix; if not,...

A USDJPY (Daily, #300) Product Settings Chart Type Time Scale Studies Draw/View *** QQ USDJPY (Daily, #300) 04/13/2022 H:126 307 L:125.334 O:125.348 C:125.650 MACD 12,26,9 MACD 2.0207 Signal 1.8847...

html sample solution

Let S = $85, K =$80,r=8% (continuously compounded), T -0.5, and 8-0. Letu -1.3,0 -0.75, and n-1. Calculate the value of a European call if A-0.652406 and B = -39.9601 a $11.001 b. $18.903 OC $15.494...