For what value of b does (A − I3)x = 0 have a nonzero solution?

0 2 b

.2 0 0

0 .5 0

The book has answer 6, not sure how to get there.

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- Nov 25th 2012, 06:16 PMtinabaker(A − I3)x = 0
For what value of b does (A − I3)x = 0 have a nonzero solution?

0 2 b

.2 0 0

0 .5 0

The book has answer 6, not sure how to get there. - Nov 25th 2012, 06:23 PMjakncokeRe: (A − I3)x = 0
ok, So a homogenous system, meaning systems of the form $\displaystyle Ax = 0 $ have a non trivial solution (non zero), only when the determinant of A is 0. So in this case

the A-I = $\displaystyle \begin{bmatrix}-1 & 2 & b \\ .2 & -1 & 0 \\ 0 & .5 & -1 \end{bmatrix} $, the determinant of this matrix is .1b-.6, so setting that equal to 0, we get .1b = .6, which means b = 6. - Nov 26th 2012, 08:04 AMtinabakerRe: (A − I3)x = 0
How can I find find a value of b without determinant?

Thank you.