Question: Show that if A is a square matrix that satisfies the equation A2 - 2A+I=0, then A-1=2I - A.

Show that if A is a square matrix that satisfies the equation A2 - 2A+I=0, then A-1=2I - A.

Step by Step Solution

★★★★★

3.38 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that A 1 2I A it suffices to sho... 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

859-L-A-L-S (2383).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(a) Show that if A is a square matrix with linearly independent columns, then A+ = A-1. (b) If A is an m n matrix with orthonormal columns, what is A+?

Q:

(a) Prove that if A is a square matrix, then A and AT have the same eigenvalues (b) Show that A and AT need not have the same eigenspaces.

Q:

(a) Show that if D is a diagonal matrix with nonnegative entries on the main diagonal, then there is a matrix S such that S2 = D. (b) Show that if A is a diagonalizable matrix with nonnegative...

Q:

(a) (5 points) For what value of n does there exist an isomorphism T:M3(R) P.(R)? a b For this value of n, write down an explicit isomorphism by defining T d e f 8 h i (b) (5 points) Suppose that a...

Q:

The formula in Problem 29 can be used to compute A 2 without an explicit matrix multiplication. It follows that without an explicit matrix multiplication and so on. Use this method to compute A 2 , A...

Q:

6. Suppose an n x n matrix A satisfies the equation A22A+l=0. Show that A3 = 3A-2l and A4=4A 3| 7. Let A be the following Matrix: u328] 4- Compute the matrices A2, AN and A'l. I Find the numbers p...

Q:

(a) If a square matrix A satisfies A 2 = A and has an inverse, show that A is the unit matrix. (b) Show that satisfies A 2 = A.

Q:

Q1 Solve the following a) Define adjoint of a Matrix A b) Show that if a square matrix A satisfies A 2 - 3A + I = 0 then A -1 = 3I - A

Q:

A Matrix Equation. ( a ) Show that if a square matrix A satisfies A 2 - 4 A + 3 I = 0 then A - 1 = 1 3 ( 4 I - A ) . ( b ) Verify these relations in the case that A = [ 2 1 1 2 ] Inverse Property....

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Refer to Problem 6-8. Disposing of incandescent light bulbs is just like getting rid of and recycling glassware in general. However, this is not the case for CFLs. Disposing of CFLs is complicated by...

Q:

Prepare a statement of cash flows for the internal service fund of the city of Boni ville from the following information: Cash on hand at the beginning of the year .. . . . . .. . . . . . $ 122...

Q:

14-10 An increase in accounts receivable is deducted from net income to obtain operating cash flows because a. cash collections increased due to increasing sales. b. cash collections from customers...

Q:

W hat are some ethical issues involved in doing research with children who might have been physically or sexually abused?

Q:

Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.) x = x +...

Q:

Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.) x = 2x -...

Q:

Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.) x 1 = x...

Q:

Assuming that the returns from holding small-company stocks are normally distributed. Assume the average annual return for holding the small-company stocks for a period of time was 18.4 percent and...

Q:

Given the following data set, show all work to calculate Q1, Q2, Q3, and the IQR. Use an appropriate calculation to determine if there are any outliers. [2K/2A] 31 22 21 21 20 20 21 20 32 28 32 29 35...

Q:

QUESTION 1 4 What did TARP, passed in October 2 0 0 8 , aim to do ? a . decrease liquidity b . increase the discount rate c . freeze financial flows d . unfreeze financial flows e . lower taxes