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Thread: Show that B=0

  1. #1
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    Show that B=0

    I would like some guidance on this question please:

    Question:Consider A = $\displaystyle \[
    \begin{pmatrix}
    2 & -5 \\
    3 & 1
    \end{pmatrix}
    \]$ and let $\displaystyle \[B= A^2 -3A+17I $
    Show that B = 0

    How do I begin answering a question like this?
    Last edited by sparky; Feb 19th 2011 at 06:55 AM.
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  2. #2
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    Quote Originally Posted by sparky View Post
    I would like some guidance on this question please:

    Question:Consider A = $\displaystyle \[
    \begin{pmatrix}
    2 & -5 \\
    3 & 1
    \end{pmatrix}
    \]$ and let $\displaystyle \[B= A^2 -3A+17I $
    Show that B = 0

    How do I begin answering a question like this?
    I hope you know how to multiply two matrices. Find $\displaystyle A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}$

    So, $\displaystyle B=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}^2-3\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}+17\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}$

    Hope you can continue.
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  3. #3
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    Ok, I figured it out:

    B = $\displaystyle \[
    \begin{pmatrix}
    2 & -5 \\
    3 & 1
    \end{pmatrix}
    \]$$\displaystyle \[
    \begin{pmatrix}
    2 & -5 \\
    3 & 1
    \end{pmatrix}
    \]$ - $\displaystyle \[
    \begin{pmatrix}
    6 & -15 \\
    9 & 3
    \end{pmatrix}
    \]$ + $\displaystyle \[
    \begin{pmatrix}
    17 & 0 \\
    0 & 17
    \end{pmatrix}
    \]$

    = $\displaystyle \[
    \begin{pmatrix}
    -17 & 0 \\
    0 & -17
    \end{pmatrix}
    \]$$\displaystyle \[
    \begin{pmatrix}
    17 & 0 \\
    0 & 17
    \end{pmatrix}
    \]$ = 0
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  4. #4
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    Thanks for your reply and assistance Sudharaka!

    Quote Originally Posted by Sudharaka View Post
    I hope you know how to multiply two matrices. Find $\displaystyle A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}$

    So, $\displaystyle B=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}^2-3\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}+17\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}$

    Hope you can continue.
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  5. #5
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    "One reason a dog is such a lovable creature is his tail wags instead of his tongue."

    Yeah, humans can be really cruel and insensitive
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