Question: full step plx 5. Let A be a square matrix and A be an eigenvalue of A. Suppose u is an eigenvector of A corresponding

full step plx

5. Let A be a square matrix and A be an eigenvalue of A. Suppose u is an eigenvector of A corresponding to A. (a) Show that u is an eigenvector of A2. What is its corresponding eigenvalue of A?? (b) Show that u is an eigenvector of A3. What is its corresponding eigenvalue of A3? (c) Let Co, C1, C2, C3 be real numbers, and B = coln + CIA + c2A2 + C343. Is u an eigenvector of B? If yes, what is the corresponding eigenvalue of B? 6. Suppose A is an n x n invertible matrix and A is an eigenvalue of A. Suppose x is an eigenvector of A corresponding to 1. (a) Show that A / 0, and x is an eigenvector of A corresponding to eigenvalue -1 (b) Define a 2n x 2n matrix C and the vector y in R2" by Is y an eigenvector of C? If yes, what is its corresponding eigenvalue

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