Question

2. Recalling that ? = 0 if and only if |A| = 0, it is clear that only singular (not invertible) matrices have 0 as an eigenvalue. Show that this holds for the following matrices, that is, find the determinants and eigenvalues of each matrix. (a) A = [1 3; 1 3] (b) A = [0 1 -1; 0 -1 1; 0 0 0]

          2. Recalling that ? = 0 if and only if |A| = 0, it is clear that only singular (not invertible) matrices have 0 as an eigenvalue. Show that this holds for the following matrices, that is, find the determinants and eigenvalues of each matrix.
(a) A = [1 3; 1 3]
(b) A = [0 1 -1; 0 -1 1; 0 0 0]

2. Recalling that ? = 0 if and only if |A| = 0, it is clear that only singular (not invertible) matrices have 0 as an eigenvalue. Show that this holds for the following matrices, that is, find the determinants and eigenvalues of each matrix.
(a) A = [1 3; 1 3]
(b) A = [0 1 -1; 0 -1 1; 0 0 0]

Added by Collin R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

07/06/2022

Step 1

Step 1:** For matrix A = $\begin{bmatrix} 1 & 3 \\ 1 & 3 \end{bmatrix}$, the determinant is calculated as follows: $det(A) = 1*3 - 3*1 = 0$ ** Show more…

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Recalling that λ = 0 if and only if |A| = 0, it is clear that only singular (not invertible) matrices have 0 as an eigenvalue. Show that this holds for the following matrices, that is, find the determinants and eigenvalues of each matrix. (a) A = (b) A =