Spectral decomposition method

Let A i) find the spectral decomposition A. if) find the spectral decomposition of A' and show that the diagonal matrix of eigenvalues is equal to the square of the matrix D found in part (i). ill) find the spectral decomposition of A-1 and show the diagonal matrix of eigenvalues is equal to the inverse of the matrix D found in part (1).1 0 3 8 LetA= 0 3 D 10+10 3 D 1 (a) Find the spectral decomposition of A. (b) Find the spectral decomposition of 3'4 = 2:0 3:11.211". Question 4 Let 1 A = -1 1 1 -1 (a) Calculate A A and find its spectral decomposition. (b) Calculate AA and find its spectral decomposition. (c) Compare the nonzero eigenvalues of A A and those of AAT.Find the spectral decomposition of es . A = 0 0 1+ Write each orthogonal projection matrix as a single matrix