4. (8%) Consider the matrix A = . Diagonalization of matrix C is denoted by QTAQ,where Q is an orthogonal matrix. is the first column of Q, please find the value of a.

1. (10%) Consider the set S = {0,1} with the operations: A binary matrixcan be generated from binary matrix. denotes an identity matrix .Suppose we have a matrix G' given byPlease use G' to find binary matrices G and H. (Hint: use reduced row echelon form)