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.
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.