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Math Help - Change of base matrix

  1. #1
    Member mybrohshi5's Avatar
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    Change of basis matrix

    Find the change-of-basis matrix from B to C

    B =  \begin{bmatrix}-1&-2&0\\1&3&2\\2&1&-7 \end{bmatrix}

    C =  \begin{bmatrix}1&-2&-1\\-1&1&-2\\0&-1&-2 \end{bmatrix}


    Change-of-basis =  C^{-1} * B

    change-of-basis from B to C =  \begin{bmatrix}-9&36&59\\4&-17&-29\\-2&8&13 \end{bmatrix}

    Does this seem right? I am a little unsure because it says from B to C so i wasnt sure if i should use the inverse of C or the inverse of B in my change-of-basis formula i listed above.

    Thank you

    p.s. if it would have been find the change-of-basis matrix from C to B would the formula i use be  B^{-1} * C ?

    Thanks for any help
    Last edited by mybrohshi5; March 30th 2010 at 03:02 PM.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by mybrohshi5 View Post
    Find the change-of-basis matrix from B to C

    B =  \begin{bmatrix}-1&-2&0\\1&3&2\\2&1&-7 \end{bmatrix}

    C =  \begin{bmatrix}1&-2&-1\\-1&1&-2\\0&-1&-2 \end{bmatrix}


    Change-of-basis =  C^{-1} * B

    change-of-basis from B to C =  \begin{bmatrix}-9&36&59\\4&-17&-29\\-2&8&13 \end{bmatrix}

    Does this seem right? I am a little unsure because it says from B to C so i wasnt sure if i should use the inverse of C or the inverse of B in my change-of-basis formula i listed above.

    Thank you

    p.s. if it would have been find the change-of-basis matrix from C to B would the formula i use be  B^{-1} * C ?

    Thanks for any help
    C^{-1}B=\begin{bmatrix}<br />
-11 & -4 & 41\\ <br />
-6 & -1 & 25\\ <br />
2 & 0 & -9<br />
\end{bmatrix}

    From C to B, you have the correct formula.
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