Find the matrix of the linear transformation T from R2 -> R² where T([1, 0]) = [1, –2] and T([2, 1) = [2, 3] %3D (Note: matrix A = [T([1, 0]), T([0, 1])] 1 -2 (a) 1 1 (c) -2 (b) -2 3 (d) 3 a C

Find the B-matrix for the transformation xAx, where B={b₁,b₂}- -5 - 1 2 = *[*) * * C A = b₁ b₂ 5 The B-matrix of the given transformation is

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.

Determine the matrix of the linear transformation T(x, y) = (3x + 5y, 3y – 2x) 5 -2 3 (a) -2 3 (b) (c) 3 3 3 (d) 3 3 -2 a 2]