step by step explanations for each operation please

Example 3.3. 2 0 0 Diagonalize the matrix A = 1 2 1 in Example 3.3.4. 1 3 2 Solution. By Example 3.3.4, the eigenvalues of A are 110: 2, 12 = 1, and lg, = 1, with 3 0 corresponding basic eigenvectors x1: =|:l,X2 , and X3 = 1 respectively. Since 0 1 1 1 0 the matrix P = [ x1 x2 X3]1 1 is invertible, Theorem 3. 3 .4 guarantees that 1 3 110 0 20 0 FWD: 0 12 0 = 01 0 =D 0 013 001 The reader can verify this directlyeasier to check AP = PD