Question

19. In each part, let TA: R2 → R2 be multiplication by A, and let u = (1, 2) and u2 = (-1,1). Determine whether the set {TA(u), TA(uz)} spans R2. 1 1 (a) A = -[ (b) A = --[- :) 0 2 2 -2

Answer 1

To determine if the set {TA(u), TA(u2)} spans R², matrix A must be applied to vectors u and u2. The resulting vectors must then be checked for linear independence. If linearly independent, they span R².

Step-by-step explanation:

The student's question pertains to linear algebra and specifically to determining whether a set of vectors spans ℝ2. The vectors in question are the images of vectors u and u2 under a linear transformation defined by multiplication with a given matrix A. The matrices provided in the question are:

(a) A = 1 1
-1 0

(b) A = 1 0
2 -2

To answer the student's question, we need to apply the matrix A to each vector (u and u2) and determine if the resultant set of vectors can span ℝ2. If the resulting vectors are linearly independent, they span ℝ2.