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**demode** This is from a cryptography related problem. I'm trying to find a 3x3 matrix in $\displaystyle \mathbb{Z}_{26}$, $\displaystyle K$, such that:

$\displaystyle K \begin{bmatrix} 0\\17\\10 \end{bmatrix} = \begin{bmatrix} 6\\2\\1 \end{bmatrix}$

$\displaystyle K \begin{bmatrix} 15\\8\\15 \end{bmatrix} = \begin{bmatrix} 0\\15\\12 \end{bmatrix}$

$\displaystyle K \begin{bmatrix} 19\\14\\12 \end{bmatrix} = \begin{bmatrix} 1\\22\\25 \end{bmatrix}$

So, could anyone please show me how to solve for K? I'm a bit confused, the only thing I'm given is what we get if we multiply K by 3 different vectors. Is there any simple systematic way to solve this?