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Suppose A is reduced by the usual row operations to

[tex]R=\begin{bmatrix}1 & 4 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0\end{bmatrix}.[/tex]

Find the complete solution (if a solution exists) to this system involving the original A:

Ax = sum of the columns of A.

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I figured if you took the columns of A and added them together, it would be the same as multiplying a by <1,1,1>. Thus I have the following:

[tex]A\mathbf{x}=A\begin{bmatrix}1 \\ 1 \\ 1\end{bmatrix}.[/tex]

So the solution is the vector <1,1,1>. Is this correct?

Thank you.