20-21 Q2; The matrix A = 0 4 o is given -20 5 , determine the...

Question

Question

20-21 Q2; The matrix A = 0 4 o is given -20 5 , determine the eigevalues and the first eigenvectors.

math Advanced-Math

Answer 1

Answer #1

Given:

2 0 -2 04 40 |-20 5

A - 17 = 0 (2 - 2) 0 -2 0 (4-2) 0 -2 0 (5-2) = 0 :: (2 - 1)(4 - ) (5 - 2) - 0 x 0) - 0(0 < (5 - 2) -0(-2))+(-2)(0 x 0 -(4-2)

1. Eigenvectors for 1 = 1 7 2 0-2 1 0 0 A - 11 = 04 0 -1 0 1 0 -2 0 5 0 0 1 2 0-2 1 0 0 04 0 0 1 0 -2 0 5 0 0 1 1 0 -2 = 0 3

2. Eigenvectors for 1 = 4 2 0-2 1 0 0 A - = 0 4 0 -4 0 1 0 -2 0 5 0 0 1 2 0-2 4 0 0 0 4 0 04 0 -2 0 5 004 -2 0-2 0 0 0 -2 0 1

3. Eigenvectors for 1 = 6 2 0-2 1 0 0 A- = 0 4 0 -6 0 1 0 -2 0 5 0 0 1 - 2 0-2 6 0 0 0 4 0 0 6 0 -2 0 5 0 0 6 -4 0-2 0 -20 -2

.

Answer 2

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