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Question 1142426: Show that the system of linear equation AX = B has a unique solution if and only if the matrix A is invertible
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! If A is a square matrix, and if A is invertible then every equation Ax = b has one and only one solution, namely x = A^(-1)b
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Note A^(-1)Ax = x = A^(-1)b
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If A is not invertible, then Ax = b will ha have either no solutions or an infinite number of solutions.
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If b = 0, then the set of all solutions to Ax = 0 is the nullspace of A
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