Find a unitary matrix P that diagonalizes the Hermitian matrix A, and determine P-¹AP. P-(-+-+-+) = A = [ 12 0 12 - 4i i] 12 + 4i -12

Find a real matrix A such that A ^6 = (09, -90)

Find the matrix A (in terms of B, C, and D) if (4DA-'B)-1 = C

The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 – 5x X3 takes the form a b. d e C e f, for some real numbers а, b, с, d, e,f. Enter these values, in order. A

Use the Gaussian algorithm to determine the inverse matrix A^-1.   A = 1  2  1 0  1   3 2  4   1

Let B be a matrix with entries  b11=2 b12=-1 b21=1 b22=-4 Find f(B)=a0In +a1B +a2B^2+....anB^n given that        f(x)=2x^2 + 4x -3

Suppose = Find an invertible matrix P and a diagonal matrix D so that A of D, and P-¹ in that order. -888888 = A = 13 5 _-12]. PDP-¹. Use your answer to find an expression for A7 in terms of P, a power -30

Given that there exists an invertible matrix PP such that D = P^{-1}APD=P−1AP, find A^{60}A60.

Find bases for row(A) and col(A) in the given matrix using A', 1-3 1 A=0 2 3 1-5 -2 row(A) col(A) 11 어 JT

Let A = (2 1, 2 3) . Find a 2 x2 matrix X so that X^2 = A.