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Problem 5 [12 marks ]: Let A be the (4 x4)-matrix displayed in cells 620-J23 of the Excel spreadsheet. Moreover, let to be the length 4 column vector displayed in cells 627-630. Use Cramer's Rule to Com- pute the third entry xs of the unique solution x =| of the matrix equation Ax = b. Problem 6 [ 2 + 8 + 2 = 12 marks ]: Let A be the ( 3 x3)- matrix displayed in cells G35-137 of the Excel Spreadsheet. Move- over, Let I be the number displayed in cell J39. You are given that det ( A - x Is) = - (x-1) ( x+1). @ Find the eigenvalues of A. 6) Find the corresponding eigenspace Eu for each eigenvalue M of A. What is the dimension of EM ? ( Diagonalize A by finding an invertible matrix P and a diagonal matrix D such that A= PDP-1 You do not need to compute podMatrix A from Problem 5 (4x4): 27 22 11 28 27 26 8 20 18 12 15 10 9 6 3 14 Vector b from Problem 5 (length 4 col.): 173 140 135 63 Matrix A from Problem 6 (3x3): 8 9 18 0 17 18 0 9 1'I Detail for the char. polynomial of A: 8