Answer Happy

2. Let {u₁, U₂} and {V₁, V2} be ordered bases for R², where H. [] and U₁ V₁ = [2] 9 U₂ V2 = ⑥ Let L be the linear transformation defined by 1,x2) T x₂) ¹ L(x) = (-x₁, and let B be the matrix representing L with respect to {u₁, U₂} [from Exercise 1(a)]. 1. Find the transition matrix S corresponding to the change of basis from {u₁, U₂} to {V₁, V₂}. 2. Find the matrix A representing L with respect to {V₁, V₂} by computing SBS-1. 3. Verify that L(v₁) = a11V1 + a21 V2 L(v₂) = a12V1 + a22V2

1. For each of the following linear operators L on R², determine the matrix A representing L with respect to {e₁, e2} (see Exercise 1 of Section 1.2) and the matrix B representing L with respect to {u₁ = (1, 1), u₂ - (-1, 1)²}: = 1. L(x) = (−x₁, x₂) T