# Thread: [SOLVED] Determine value of variables in a matrices

1. ## [SOLVED] Determine value of variables in a matrices

Hello,

I have what I think is a solution, but I'm not sure. I would certainly appreciate any help. Here is the problem:

Determine the value of each variable.

$\displaystyle \left( {\begin{array}{*{20}{c}} {x + 3} & {y + 4} \\ 7 & { - 1} \\ \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 6 & 0 \\ 7 & k \\ \end{array}} \right)$

My answer is x=3, y=3. Is that correct?

2. Originally Posted by majax79
Hello,

I have what I think is a solution, but I'm not sure. I would certainly appreciate any help. Here is the problem:

Determine the value of each variable.

$\displaystyle \left( {\begin{array}{*{20}{c}} {x + 3} & {y + 4} \\ 7 & { - 1} \\ \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 6 & 0 \\ 7 & k \\ \end{array}} \right)$

My answer is x=3, y=3. Is that correct?
Look at the corresponding components.

$\displaystyle x + 3 = 6$

$\displaystyle y + 4 = 0$

$\displaystyle 7 = 7$

$\displaystyle -1 = k$.

Solve for $\displaystyle x, y, k$.

3. Just equate positions from one matrix to the other

$\displaystyle x+3=6$

$\displaystyle y+4=0$

$\displaystyle k=-1$

Spoiler:
$\displaystyle x=3, y=-4, k=-1$

4. I just tried to solve the sum ..Is the solution x=3 and y=-4 correct for the above sum "Prove it"??

5. Yes. And it should be obvious that $\displaystyle k = -1$.