Question: Let A be an m n matrix. Prove that every vector x in R n can be written in the form x = p

Let A be an m × n matrix. Prove that every vector x in Rⁿ can be written in the form x = p + u, where p is in Row A and u is in Nul A. Also, show that if the equation Ax = b is consistent, then there is a unique p in Row A such that Ap = b.

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To prove that every vector x in Rn can be written in the form x p u where p is in Row A and u is in Nul A we need to show that x belongs to the row sp... View full answer

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