(15 pts) Let n be a positive integer. Let A, B, S be square matrices of size n. Suppose S is invertible and S-¹AS = B. (

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15 Pts Let N Be A Positive Integer Let A B S Be Square Matrices Of Size N Suppose S Is Invertible And S As B 1 (41.44 KiB) Viewed 43 times

(15 pts) Let n be a positive integer. Let A, B, S be square matrices of size n. Suppose S is invertible and S-¹AS = B. (a) Show that if x is an eigenvector of A with eigenvalue A, then S-¹x is an eigenvector of B with eigenvalue (b) Show that for any positive integer k, (A-AI) is similar to (B-In)*. (c) Using part (b), or otherwise, show that [1 1 0 0] [1 1 0 0 0110 C = 0 1 0 0 0 0 1 1 0010 0 0 0 1 0001 are not similar. > D =