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$$a\begin{bmatrix} 2 & 6 \\ 1 & 4 \end{bmatrix} = \begin{bmatrix} x & 27 \\ y & z \end{bmatrix}$$ Is it possible to evaluate the value of x+z?

I can see in this math that there are three known variables, but If I am asked to find a numeric value of x+z then how to do it?

Any suggestion?

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    $\begingroup$ There seem to be four variables in that problem: $a,x,y$ and $z$. Unless $a$ is not meant to represent a scalar? $\endgroup$
    – mweiss
    Commented Dec 8, 2015 at 5:24
  • $\begingroup$ what does $a$ mean? $\endgroup$
    – Ronald
    Commented Dec 8, 2015 at 5:25
  • $\begingroup$ Sorry yes four variables. What I assumed first that,, I could find it easily considering simple matrix manipulation but I couldn't. $\endgroup$ Commented Dec 8, 2015 at 5:28

2 Answers 2

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From what you've written, it looks like you have four equations in four variables:

  1. $2a = x$
  2. $6a = 27$
  3. $a = y$
  4. $4a = z$

Solve the system!

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Note that $a\times 6=27$ which implies that $a=\frac{27}{6}$ and $y=a=\frac{27}{6}$. Moreover, $x+z= a(2+4)=\frac{27}{6}\times 6=27$.

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