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How do you find a solution to a matrix $A$ that minimizes $\|x\|$ when $A^TA$ is not invertible? The matrix is $$A = \pmatrix{1 &1&2&2\\1&2&3&4}$$

I don't know if this helps but also in the question above this one, we are asked to find all solutions to $Ax = \pmatrix{0\\11}$

Thank you.

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    The number of elements in row 1 and row 2 of A are not the same. There is a typo either in the first or the second row.2011-11-04
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    sorry the second row is comprised of [1 2 3 4] without the 02011-11-04
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    Is this question also supposed to assume that $Ax=\pmatrix{0\\1}$? Something else is needed, otherwise, $x=0$ is a trivial solution.2011-11-04

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