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Math Help - (A − I3)x = 0

  1. #1
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    (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.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: (A − I3)x = 0

    ok, So a homogenous system, meaning systems of the form  Ax = 0 have a non trivial solution (non zero), only when the determinant of A is 0. So in this case
    the A-I =  \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.
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  3. #3
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    Re: (A − I3)x = 0

    How can I find find a value of b without determinant?

    Thank you.
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