Consider the linear transformation T: R? → R³: X2 ((:)- X1 -5x1 + 13x2 -7x1 + 16x2 T X2 Write down the matrix Mg.g (T) of the transformation T if the bases B of R? and B' of R³ are specified as -{(;) (:)} B : and {(:) ( B' 2 2

Let T : P3 → P3 be the linear transformation such that T(-2x²) = 3x² + 3x, T(-0.5x + 3) = 3x? + 4x – 1, T(5x² + 1) = -3x + 1. Find T(1), T(x), T(x²), and T(ax? + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =

2 [1], 0₂ = [1] · ₁ = [3], and y₂ = [¯ ] - 5 6 R² be a linear transformation that maps e₁ into y₁ and 19. Let e₁ = T: R² maps e2 into y2. Find the images of [3] -3 and [2]. x2 and let

Find the matrix of the linear transformation T from R? R?, where T([1, 0]) = [1, -2], and T([2, 1]) = [2, 3] (Note: matrix A = [T([1,0]), T([0, 1])] ). 1 (a) 1 (b) 1. (c) -2 1 -2 3 -2 1 (d) 0. 3