The matrices [8]. A₂ = [] ^--^-i [] , A4 = form a basis for the linear space V = R 2x2. Write the matrix of the linear transformation T: R2x2 →R 2x2 T(A) = 3A + 10AT relative to this basis. such that A₁ = A3 =

Find the matrix representation of the linear operator T relative to B1. Then use Theorem 15 to find [T]B2

Use matrix multiplication to find the contraction of (a, b) with factor k = 1/α, where α > 1.

4a). The transformation defined by the matrix A = [14 5 stretches images in R² in the directions y = x and y = -x. Figure out the factor by which anything in the y = x direction is stretched and the factor by which anything in the y = -x direction is stretched. 4b). The transformation defined by the matrix B = -82 -55 13 3] stretches images in R2 in one direction by a factor of 3 and some other direction by a factor of 2. Figure out what direction gets stretched by a factor of 3 and what direction gets stretched by a factor of 2. 4c). The transformation defined by the matrix C = stretches images in R2 in two directions. Find the directions and the factors by which it stretches in those directions.