Let A be a matrix that satisfies ?^2 =? where ? is the identity matrix. a. Find a 2x2 example of such a matrix that is not 1 0 0 1 or -1 0 0 -1 b. Prove that, in general (i.e, any size), any matrix that satisfies ?^2 =? must be invertible. c. Explain why it must be the case that ?^−1 =?.

Q: Table Q4(b) is generated from the function f(x)=e* – 4x² + B , where B is the last two digits of…

A: here question has a mistake , though I correct it and solve it for you, here two different f(x) is…

Q: _Let A = -3 -1 1 2 -12 0 0 -1 5 If possible, find an invertible matrix P so that D = P-¹AP is a…

A: Let us strat by finding the eigen values of the matrix…

Q: If A is an nxn matrix, then the equation Ax = b has at least one solution for each b in R".

A: (C)

Q: 04) X = [ Y = ; Hand Z = [ 3 Q.4) X Prove the Distributive laws of multiplication over Subtraction…

A: The given matrices are X=23-10,Y=0131  and  Z=22-10. The distributive law of multiplication over…

Q: Show that any 3 × 3 matrix of the form ⎧ ⎩ a 1 0 0 a 1 0 0 b ⎫ ⎭ is defective.

A: We have to show that given matrix is defective.

Q: eness of the following 3 (a) A = 3 -1 -4 -1 1 -1 6 0 -2 -1 (b) В %— -2

A: RULES: The pivot elements of a symmetric matrix A are the eigenvalues of the matrix A. A is…

Q: 1 1 1 0100 0120 00 0 Let A = Write A as C DC , where D is a diagonal matrix. Hint: You can always…

A: Given : matrix A=1110010001200000 We have to write A as CDC-1, where D is a diagonal matrix.

Q: 2. a) Let A = answer. [2]. Find the matrices A² and A³. What can be the matrix A"? Justify your -11

A:

Q: (b) Table Q4(b) is generated from the function ƒ(x)= e* - 4x² + B , where B is the last two digits…

A: Given: fx=ex-4x2+B To find: f'1.5

Q: Find an invertible matrix X and a diagonal matrix D such that X-1 AX = D. You don't need to compute…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Is the following matrix 'B' diagonalizable?

A:

Q: Let A be a 5 x 3 matrix and assume that N(A) is trivial, i.e.. N(A) = {0}. Find dim C(A).

A: Given that A be a 5*3 matrix. and N(A)={0}. we have to find the dim C(A)?

Q: If D = diag(2, -1, 0) and M is a 3 x 3 matrix, describe how the rows and/or columns of DM are…

A: Given thatdiag and M is 3×3 matrixWe have to describe how the rows and/or columns of DM related to…

Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positive x-axis and…

A: Let a vector be defined as: a=x, y. The magnitude of a is calculated using the formula: r=x2+y2.…

Q: 1. Say either true or false in cach of the statements below, and prove cach assertion. (a) The…

A:

Q: Properties of Transpose If r is a scalar and A and B are matrices of the appropriate sizes, then 1.…

A:

Q: Now write ageneric exampledaux2 motrix a with entries paying close attention to the subscripts है…

A: Generic Example of a 4×2 matrix  Let A be a 4×2  matrix. For any entry,aij i represents the ith row,…

Q: [0 0 01 10. Let A=100. Show that A³=0. Use matrix algebra to compute the product of Lo 1 ol…

A:

Q: 6. 1 4 If w = -3 E span 2 then x = 1 4 3 Select one: True 21 False

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: P= Let A = -3 0 0 9 36 -24 12 4 -11 Find an invertible matrix P and a diagonal matrix D such that D…

A: Eigenvalue: A number λ is said to be an eigenvalue of a matrix A if there exists a non-zero vector x…