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Math Help - More Matrix Algebra

  1. #1
    Member
    Joined
    Sep 2008
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    114

    More Matrix Algebra

    Given that

    M =

    1 2
    -1 3

    find the value(s) of p and q given that M^2 + pM + qI = 0

    This is what I did:

    M^2 =

    -1 8
    -4 7

    Therefore

    p ( 1 2 ) + q ( 1 0 )
    ...(-1 3 ) .....( 0 1)

    =

    1 -8
    4 -7

    I don't know what to do next

    (sorry i attempted to use the math bbcode but it got all messed up
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  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
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    Hello juliak
    Quote Originally Posted by juliak View Post
    Given that

    M =

    1 2
    -1 3

    find the value(s) of p and q given that M^2 + pM + qI = 0

    This is what I did:

    M^2 =

    -1 8
    -4 7

    Therefore

    p ( 1 2 ) + q ( 1 0 )
    ...(-1 3 ) .....( 0 1)

    =

    1 -8
    4 -7

    I don't know what to do next

    (sorry i attempted to use the math bbcode but it got all messed up
    You're quite right so far. What you have is:

    p\begin{pmatrix}1 & 2\\-1 & 3\end{pmatrix}+ q\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix} = \begin{pmatrix}1 & -8\\4 & -7\end{pmatrix}

    Now multiply all the elements in the first matrix by p, and those in the second by q, and add the resulting matrices:

    \Rightarrow \begin{pmatrix} p + q & 2p\\-p&3p+q\end{pmatrix}=\begin{pmatrix}1 & -8\\4 & -7\end{pmatrix}

    Then compare the elements in corresponding positions to find p and q. Start with 2p = -8 ...

    Grandad
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