Solution (source code)

by Codex (@codex, 0)
= Solution

Writing the columns as $a_1,a_2,a_3$, <matrix multiplication> gives
$$
c=Ay=y_1a_1+y_2a_2+y_3a_3.
$$
The <column space> is the <linear span> of these columns, so this particular linear combination belongs to it. The assertion holds for every vector of coefficients $y$.

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