Linear Algebra

Directions: Answer the following problems below. In return, I will give you a good rating. Thank you so much!

Note: Please be careful with the calculations in the problem. Kindly double check the answer if there is a deficiency. And also, please box the final answer. Thank you!

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5. DETAILS LARLINALG8 7.1.001. Verify that 1, is an eigenvalue of A and that x; is a corresponding eigenvector. A = 0 - 2 1' M1 = 2, X1 = (1, 0) 12 = -2, X2 = (0, 1) Ax1 = 3 2][8] - = 2 = A1X1 Ax2 Submit Answer6. DETAILS LARLINALGB 7.1.021. Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces} of the matrix. 2 2 7 D 3 2 D 1 2 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (31; 32; 33) =( ) a basis for each of the corresponding eigenspaces Submit Answer 7. DETAILS LARLINALGB 7.1.019. Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces} of the matrix. 3 1 2 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (11i/12]=( ) a basis for each of the corresponding eigenspaces X1: X2 Submit