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Math Help - Matrices

  1. #1
    Newbie
    Joined
    Dec 2007
    Posts
    9

    Matrices

    I am going crazy. it is almost 3:00 in the morning and I have been trying to figure out a problem and I just can't get it.

    If you could show me how I would so appreciate it. Iam taking an online math class and the teacher has 7 other classes and never seems to answer the questions on time. Thank you so much!

    A =
    • 2 0 1
    • 2 -1 3
    • 4 1 2

    B =
    • -2 1 0
    • 4 3 -2
    • 1 2 -1

    I need to find (A + B)squared

    2 + -2 0 + 1 1 + 0 is 0 1 1

    and then squared is the same answer

    The book has the answer as

    Matrix

    • 11 5 2
    • 17 13 9
    • 23 14 9
    I know this is difficult to read but I hope you can understand it. i didn't know how to type any other way
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  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    \displaystyle A+B=\begin{pmatrix}<br />
2 & 0 & 1\\<br />
2 & -1 & 3\\<br />
4 & 1 & 2\end{pmatrix}+<br />
\begin{pmatrix}<br />
-2 & 1 & 0\\<br />
4 & 3 & -2\\<br />
1 & 2 & -1\end{pmatrix}=<br />
\begin{pmatrix}<br />
0 & 1 & 1\\<br />
6 & 2 & 1\\<br />
5 & 3 & 1\end{pmatrix}
    Then, (A+B)^2=\begin{pmatrix}<br />
11 & 5 & 2\\<br />
17 & 13 & 9\\<br />
23 & 14 & 9\end{pmatrix}
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  3. #3
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    \left(\begin{bmatrix}<br />
{2}\;\; {0}\;\;{1}\\<br />
{2}\;\;{-1}\;\;{3} \\<br />
{4}\;\;{1}\;\;{2}<br /> <br />
\end{bmatrix} +\begin{bmatrix}<br />
{-2}\;\; {1}\;\;{0}\\<br />
{4}\;\;{3}\;\;{-2}\\<br />
{1}\;\;{2}\;\;{-1}\\<br /> <br />
\end{bmatrix}\right)^2

    =\left(\begin{bmatrix}<br />
{2-2\ }\;\; {\ 0+1\ }\;\;{\ 1+0}\\<br />
{2+4\ }\;\;{\ -1+3\ }\;\;{\ 3-2}\\<br />
{4+1\ }\;\;{\ 1+2\ }\;\;{\ 2-1}\\<br /> <br />
\end{bmatrix}\right)^2

    =\left(\begin{bmatrix}<br />
{0}\;\;{1}\;\;{1}\\<br />
{6}\;\;{2}\;\;{1}\\<br />
{5}\;\;{3}\;\;{1}\\<br />
\end{bmatrix}\right)^2

    =\begin{bmatrix}<br />
{0}\;\;{1}\;\;{1}\\<br />
{6}\;\;{2}\;\;{1}\\<br />
{5}\;\;{3}\;\;{1}\\<br />
\end{bmatrix} \cdot \begin{bmatrix}<br />
{0}\;\;{1}\;\;{1}\\<br />
{6}\;\;{2}\;\;{1}\\<br />
{5}\;\;{3}\;\;{1}\\<br />
\end{bmatrix}

    =\begin{bmatrix}<br />
{0\cdot 0 + 1 \cdot 6 +1\cdot 5\ }\;\;{\ 0\cdot 1+1\cdot 2 + 1 \cdot 3\ }\;\;{\ 0\cdot 1+1\cdot 1 + 1\cdot 1}\\<br />
{6\cdot 0 + 2 \cdot 6 + 1 \cdot 5\ }\;\;{\ 6\cdot 1+2\cdot 2 + 1 \cdot 3\ }\;\;{\ 6\cdot 1 +2 \cdot 1 + 1 \cdot 1}\\<br />
{5\cdot 0+ 3 \cdot 6 + 1 \cdot 5\ }\;\;{\ 5 \cdot 1 + 3 \cdot 2 + 1 \cdot 3\ }\;\;{\ 5 \cdot 1 + 3 \cdot 1 + 1 \cdot 1}\\<br />
\end{bmatrix}

    =\begin{bmatrix}<br />
{11}\;\;{5}\;\;{2}\\<br />
{17}\;\;{13}\;\;{9}\\<br />
{23}\;\;{14}\;\;{9}\\<br />
\end{bmatrix}
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  4. #4
    Newbie
    Joined
    Dec 2007
    Posts
    9

    Thank you so very much Divideby0

    I knew there was an easy explaination. I just couldn't for the life of me figure it out. Next time I am just going to come here and post because I really do not like staying up till all hours of the night.

    Thank you again really!

    Lori
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