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Math Help - 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 = \[<br />
 \begin{pmatrix}<br />
  2 & -5 \\<br />
  3 & 1<br />
 \end{pmatrix}<br />
\] and let \[B= A^2 -3A+17I
    Show that B = 0

    How do I begin answering a question like this?
    Last edited by sparky; February 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 = \[<br />
 \begin{pmatrix}<br />
  2 & -5 \\<br />
  3 & 1<br />
 \end{pmatrix}<br />
\] and let \[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 A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}

    So, 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 = \[<br />
 \begin{pmatrix}<br />
  2 & -5 \\<br />
  3 & 1<br />
 \end{pmatrix}<br />
\] \[<br />
 \begin{pmatrix}<br />
  2 & -5 \\<br />
  3 & 1<br />
 \end{pmatrix}<br />
\] - \[<br />
 \begin{pmatrix}<br />
  6 & -15 \\<br />
  9 & 3<br />
 \end{pmatrix}<br />
\] + \[<br />
 \begin{pmatrix}<br />
  17 & 0 \\<br />
  0 & 17<br />
 \end{pmatrix}<br />
\]

    = \[<br />
 \begin{pmatrix}<br />
  -17 & 0 \\<br />
  0 & -17<br />
 \end{pmatrix}<br />
\] \[<br />
 \begin{pmatrix}<br />
  17 & 0 \\<br />
  0 & 17<br />
 \end{pmatrix}<br />
\] = 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 A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}

    So, 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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