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A matrix equation has the same solution set as the vector equation which has the same solution set as the linear system

REVIEW. A matrix equation has the same solution set as the vector equation which has the same solution set as the linear system whose augmented matrix is. Therefore: A x = b has a solution if and only if b is a linear combination of columns of A. REVIEW. Theorem 4:

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A matrix equation has the same solution set as the vector equation which has the same solution set as the linear system