How Can I solve for a vector by multiplying the matrix inverse for non invertible matrix?

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I have the followingenter image description here equation I need to find {N} what I did is : multiply both sides by [X1 X2 ....]' then I multiply both side by the inverse of the multiplication inv([X1 X2 ....]'[X1 X2 ....]) but I couldn't find the {N} vector. I guess because if m<n , the matrix ATA is not invertible.

is there a way to solve for my {N} vector ?