Find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x, = (1,0,0,0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector. 1 2 7 7 5 14 15 13 A = -5 2 0 5 9 4 8 2 a. The largest eigenvalue is approximately (Do not round until the final answer. Then round to four decimal places as needed.)

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Find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x, = (1,0,0,0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector.
1 2 7 7
5 14 15 13
A =
-5 2 0 5
9 4 8 2
a. The largest eigenvalue is approximately
(Do not round until the final answer. Then round to four decimal places as needed.)
Transcribed Image Text:Find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x, = (1,0,0,0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector. 1 2 7 7 5 14 15 13 A = -5 2 0 5 9 4 8 2 a. The largest eigenvalue is approximately (Do not round until the final answer. Then round to four decimal places as needed.)
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