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