Question

Find the eigenvalues and the corresponding eigenvectors of The Matrix:

Answer 1

Answer:

| 1 -1 2 |

A = | 0 1 0 |

| 1 2 1|

|A-kI| = 0 =>| 1 -1 2 | | 1 0 0| => 0

| 0 1 0 | -k | 0 1 0|

| 1 2 1| | 0 0 1|

| (1-k) -1 2 |

| 0 (1-k) 0| => 0 =>

| 1 2 (1-k)|

$(1 - k)((1 - k) \times (1 - k) - 0 \times 2)$

$- 0( - 1(1 - k) - 4) +$

$1( - 1 \times 0 - 2(1 - k)) = 0 = >$

${(1 - k)}^{3} - 2(1 - k) = 0 = >$

${(1 - k)}^{2} (1 - k - 2) = 0 = >$

${(1 - k)}^{2} ( - 1 - k) = 0 = >$

k = -1 or 1. Hope it helps you.