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# Please help with this question asap Linear Algebra

Q5 Eigenmatrix8 PointsLetM2 =211 12212 22: ij ERbe the vector space of 2 X 2 real matrices with entrywise addition and scalar multiplication.Consider the subspaceW = {XEM2 : X = XT]of M2 consisting of symmetric matrices.(a) (2pts) Find a basis of W. What is its dimension?(b) (2pts) Let A =1 1. Show that if X E W then AXA EW.(c) (4pts) Consider the linear transformation T : W - W defined byT(X) = AXA,where A is the same matrix from part (b). Find an eigenvector of T with strictly positiveeigenvalue (i.e., a nonzero solution to the equation T(X ) = XX with > > 0).