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- Apr 14, 2013

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We have tha matrix \begin{equation*}A:=\begin{pmatrix}1 & 5 & 8 & 2 \\ 2 & 4 & 6 & 0 \\ 3 & 3 & 8 & 2 \\ 4 & 2 & 6 & 0 \\ 5 & 1 & 8 & 2\end{pmatrix}\in \mathbb{R}^{5\times 4}\end{equation*}

Determine a basis $B$ of $\mathbb{R}^4$ and a basis $C$ of $\mathbb{R}^5$ such that $M_C^B(A)$ contains at the left upper corner the unit matrix and everywhere else zeroes.

Could you give me a hint for that?

Do we have to write each column of $A$ as a linear combination of $C$ and the corresponding coefficients have to satisfy the desired form that $M$ will have?