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February 1st, 2015, 01:03 PM   #1
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Matrices Problem

I didn't know how to type it in latex code so I just took a picture of my problem.

I'm having trouble with number 9.

View image: 10951891 922790067739203 1006049733 n

I'm familiar with addition/subtraction and multiplication. A hint would be greatly appreciated
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February 1st, 2015, 01:40 PM   #2
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[A][B] + [C] = [D]

[A][B] = [D] - [C]

subtract C from D on the right side to get a single 2 x 2 matrix

multiply matrices A and B to get a single 2 x 2 matrix

match up the coefficients of the resulting two matrices & solve
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February 1st, 2015, 01:49 PM   #3
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Hi I did everything except for the last part. I'm afraid I don't understand what you mean by matching up the coefficients. Thanks
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February 1st, 2015, 03:13 PM   #4
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Hello, BonaviaFx!

Quote:
If $\,\begin{pmatrix}a&b\\c&d\end{pmatrix} \begin{pmatrix}2&\text{-}1\\3&5\end{pmatrix} + \begin{pmatrix}4&1\\0&3\end{pmatrix} \;=\;\begin{pmatrix}12&10 \\ \text{-}7 & 0 \end{pmatrix}$

find $a,b,c,d.$

$\quad \begin{pmatrix}2a+3b & \text{-}a+5b \\ 2c+3d & \text{-}c + 5d\end{pmatrix} + \begin{pmatrix}4&1\\0&3\end{pmatrix} \;=\;\begin{pmatrix}12&10\\\text{-}7&0\end{pmatrix}$

$\quad \begin{pmatrix}2a+3b+4 & \text{-}a+5b+1 \\ 2c+3d+0 & \text{-}c+5d+3\end{pmatrix} \;=\;\begin{pmatrix}12&10 \\ \text{-}7&0 \end{pmatrix}$

$\quad \begin{array}{ccccccccc} 2a+3b+4 \:=\:12 && \text{-}a + 5b + 1 \:=\:10 \\ 2c + 3d + 0 \:=\:\text{-}7 && \text{-}c+5d + 3 \:=\:0 \end{array}$


Solve the systems:

$\quad \begin{array}{c}2a + 3b \:=\:8 \\ \text{-}a + 5b \:=\:9\end{array} \qquad\begin{array}{c}2c+3d \:=\:\text{-}7 \\ \text{-}c+5d \:=\:\text{-}3\end{array}$

Therefore: $\:\begin{pmatrix}a&b\\c&d\end{pmatrix} \;=\; \begin{pmatrix}1&2 \\ \text{-}2&\text{-}1 \end{pmatrix}$

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February 2nd, 2015, 10:14 AM   #5
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oh dam I had to do solve them simultaneously? That explains a lot thanks !
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