Given that,Determine the 2 × 2 matrices X and Y satisfyingi. AX = B;ii. Y A = B. (6)

Consider the matrices and  .Calculate .

Let A = (a) be the 2x2 matrix of reflection in the x-axis followed by reflection in the line y = x.Find a12

Solve for X using the matrices below.2A + 4B = −2XA = 6 −5 7 03 −4 and B = 0 7 8 0−4 −1.X =

Context: [Linear Algebra] 6. For which conditions on b = (b1, b2, b3, b4) do there exist solution(s) for the linear system Ax = b? (a) A = [ 2 4 1 8 / 4 8 2 10 / 1 2 0 3 / 8 10 4 14] (b) A = [2 2 2 2 2 2 / 4 4 2 4 6 6 / 1 2 2 0 1 1 / 8 8 8 8 8 8]. Note that (a) is a 4x4 matrix and (b) is a 4x6 matrix. Please answer in concise format that's easy to read.

1. For the matrix 𝐵𝐵 = �1 2 −2−1 0 14 3 1�finda) B 2 = B×B