# Solve for $X$ in a simple equation system.

$$\left[ \begin{array}{ccc} 0 & -6 & 4\\ 1 & 2 & 7\end{array} \right] = 4X + 5 \left[ \begin{array}{ccc} 3 & 4 & 3\\ 8 & -4 & 8\end{array} \right]$$

First, how should i read this? Secondly how do I procede and solve for $X$, a full development would be very much appreciated!

Thank you kindly for you help!

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Two matrices are the same when all of their values are the same.
Lets call $$X=\begin{pmatrix} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \end{pmatrix}$$ So your equations are \begin{align*} 0&= 4 x_{11} +5 \cdot 3\\ -6&= 4 x_{12} + 5 \cdot 4\\ 4&=4 x_{13} + 5 \cdot 3\\ 1&= 4 x_{21} + 5\cdot 8\\ 2&= 4x_{22} + 5 \cdot (-4)\\ 7&= 4x_{23} + 5 \cdot 8 \end{align*} Just solve those and write what $X$ is.

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Thank you very much for the excellent answer! I understand how this should be done now. –  Lukas Arvidsson Mar 15 '13 at 7:40
You are welcome :) –  Dominic Michaelis Mar 15 '13 at 7:43
You must see $X$ as a matrix of size $2\times 3$ and then you have $$X=\frac{1}{4}\left(\left[ \begin{array}{ccc} 0 & -6 & 4\\ 1 & 2 & 7\end{array} \right] - 5 \left[ \begin{array}{ccc} 3 & 4 & 3\\ 8 & -4 & 8\end{array} \right]\right),$$ and you do the calculations on the components.