MathAlgebraLinear algebraMatrix decomposition

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Approximating the solution

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The linear system given by:

A=(1236)b=(21)A= \begin{pmatrix} 1 & 2 \\ 3 & 6 \\ \end{pmatrix} \qquad \mathbf{b}= \begin{pmatrix} 2 \\1 \\ \end{pmatrix}has no solution. Find the vector in Im(A)\operatorname{Im}(A) that is as closest to b\mathbf{b}. Write its entries multiplied by 2, separated by a space.

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