Question: eigenmatrix question, not sure how to approach the question Q5 Eigenmatrix 8 Points Let M2 = 11 12 21 C 22 : Mij ER be

eigenmatrix question, not sure how to approach the question

Q5 Eigenmatrix 8 Points Let M2 = 11 12 21 C 22 : Mij ER be the vector space of 2 X 2 real matrices with entrywise addition and scalar multiplication. Consider the subspace W = {XEM2 : X = XT] of M2 consisting of symmetric matrices. (a) (2pts) Find a basis of W. What is its dimension? (b) (2pts) Let A = show that if X E W then AXA EW. (c) (4pts) Consider the linear transformation T : W - W defined by T(X) = AXAT. Find an eigenvector of T with strictly positive eigenvalue (i.e., a nonzero solution to the equation T(X) = XX with > > 0). Please select file(s) Select file(s)

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