# Matrix Equation, Solving for Variables.

I'm going through my exercises, and came across a problem that wasn't covered in our lectures. Here's the question:

\begin{align} \begin{bmatrix} a-b & b+c\\ 3d+c & 2a-4d \end{bmatrix} \end{align} = \begin{align} \begin{bmatrix} 8 & 1\\ 7 & 6 \end{bmatrix} \end{align}

What I have done so far is:

\begin{align} \begin{bmatrix} a-b-8 & b+c-1\\ 3d+c-7 & 2a-4d-6 \end{bmatrix} \end{align} = \begin{align} \begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix} \end{align}

And the solving for variables,

$$a-b-8 = 0$$ $$a-b = 8$$ $$a = \frac{8}{-b}$$

$$b+c-1=0$$ $$b+c=1$$ $$b=\frac{1}{c}$$

$$3d+c-7=0$$ $$3d+c=7$$ $$3d=\frac{7}{c}$$ $$d=\frac{7}{3c}$$

$$2a-4d-6=0$$ $$2a-4d=6$$ $$\frac{16}{-2b}-\frac{28}{12c}=6$$

-
Whoa. Yes, quite a few very basic mistakes here. In fact, every single one of your subproblems is wrong; you are dividing when you should be subtracting. I hope you will not take offense but I would strongly recommend a conference with your instructor. –  Michael C. Grant May 22 '13 at 2:48
+1 for showing your work. –  response May 22 '13 at 2:51
@MichaelC.Grant No none taken, we haven't done anything like this in our labs or during the lectures, and I was just guessing as to what I should be doing. –  user1327636 May 22 '13 at 2:55
Cool. It does seem rather unfortunate that they would foist this multiequation problem on you before you had mastered isolating variables in single equations. –  Michael C. Grant May 22 '13 at 2:59
I'm taking this course during our Spring semester, and it's normally a 4 month long class, however during the Spring it's crammed down into only 2 months. So this is most likely why we are skipping some of these types of questions. Thank you for your feedback though, I appreciate it. –  user1327636 May 22 '13 at 3:01

Error 1: $a-b=8$ is not the same as $a = \frac{8}{-b}$ but $a = 8 + b$

Error 2: $b+c=1$ is not the same as $b = \frac{1}{c}$ but $b = 1-c$

Error 3: $3d+c=7$ ... same as errors 1 and 2

Error 4: $2a-4d=6$ Incorrect substitution because of previous errors. Fix the previous errors and then subsititue to fix this error

-
\begin{align} \begin{bmatrix} 1 & -1 & 0 & 0\\ 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 3 \\ 2 & 0 & 0 & -4 \\ \end{bmatrix} \end{align} \begin{align} \begin{bmatrix} a \\ b \\ c \\ d \\ \end{bmatrix} \end{align} = \begin{align} \begin{bmatrix} 8 \\ 1\\ 7 \\ 6 \end{bmatrix} \end{align}