My Math Forum Matrices Problem

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 February 1st, 2015, 01:03 PM #1 Senior Member     Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 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
 February 1st, 2015, 01:40 PM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 2,976 Thanks: 1571 [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 Thanks from BonaviaFx
 February 1st, 2015, 01:49 PM #3 Senior Member     Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 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
February 1st, 2015, 03:13 PM   #4
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

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

 February 2nd, 2015, 10:14 AM #5 Senior Member     Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 oh dam I had to do solve them simultaneously? That explains a lot thanks !

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