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Please show steps with explanation and I'll rate 1. Determine the existence and uniqueness of solutions for each of the following systems of linear equations.

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1. Determine the existence and uniqueness of solutions for each of the following systems of linear equations. If a unique solution exists, find it. If infinitely many solutions exist, find the space of all solutions as well as the one with smallest Euclidean norm ( x||. If no solutions exist, find the vector x that gives the smallest error || Ax - bll. (i) A b 2 3 -1 = 0 (ii) -1 - 352 1 21+ 1= 0 3 1 (iii) A 3 5 with same b as in (i). 2 4

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