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Math Help - Linear Algebra And Matrices. lines

  1. #1
    Dani
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    Linear Algebra And Matrices. lines

    I am stuck on the following problems, both from university intro algebra course

    Find the parametric equations of the line which intersects each of followinglines orthogonally: x=-9+3t , y=-5+t , z=-3+t and x=-3+2t , y=-7+3t , z=-17+t

    Other question

    If A is a matric satisfying
    -8(A^3)-10(A^2)+8A+I=0
    show that A is invertible with
    (A^-1)=-1(-8(A^2)-10A+8I)

    Im assuming that I is the identity matrix but other than that im lost.
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  2. #2
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    Quote Originally Posted by Dani View Post
    I am stuck on the following problems, both from university intro algebra course

    Find the parametric equations of the line which intersects each of followinglines orthogonally: x=-9+3t , y=-5+t , z=-3+t and x=-3+2t , y=-7+3t , z=-17+t
    .
    The aligned vector with the first line is,
    \bold{u}=3\bold{i}+\bold{j}+\bold{k}
    The aligned vector with the second line is,
    \bold{v}=2\bold{i}+3\bold{j}+\bold{k}
    To be both orgothonal we need a vector orthogonal to both, for example, the cross product vector,
    \bold{u}\times \bold{v}=\left| \begin{array}{ccc}\bold{i}&\bold{j}&\bold{k}\\3&1&  1\\2&3&1 \end{array} \right|=-2\bold{i}-\bold{k}+7\bold{k}
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