Suppose that A is a square matrix and there is a vector, b, such that LS(A, b)

Question:

Suppose that A is a square matrix and there is a vector, b, such that LS(A, b) has a unique solution. Prove that A is nonsingular. Give a direct proof (perhaps appealing to Theorem PSPHS) rather than just negating a sentence from the text discussing a similar situation.