Q51 - Math 330 Quiz 5.1 Friday April 3, 2009 The following...

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Unformatted text preview: Math 330 Quiz 5.1 Friday April 3, 2009 The following matrix has 11 as an eigenvalue. Find the associated eigenspace. 12 1 3 A = 2 12 -1 13 7 8 SOLUTION: 11 being an eigenvalue means that there is a nonzero x such that Ax = 11x (A - 11I)x = 0 Which means finding x is equivalent to finding the null space of A - 11I: 1 1 3 1 1 3 1 1 3 (R2,R3)(R2-2R1,R3-13R1) R2-R2 = 0 1 7 2 1 -1 0 -1 -7 0 -6 -42 0 -6 -42 13 7 -3 1 0 -4 1 1 3 R3R3+6R2 R1R1-R2 = 0 1 7 = 0 1 7 0 0 0 0 0 0 x1 So we have that with x = x2 that x3 x1 - 4x3 x2 + 7x3 x1 = 4x3 4 x1 = 0 = x2 = -7x3 = x2 = x3 -7 = 0 1 x3 = x3 x3 So our associated eigenspace of A for eigenvalue 11 is just Span 4 -7 1 1 ...
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