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Consider a system of linear equations with augmented matrix A and coefficient matrix C. In each...

  1. Consider a system of linear equations with augmented matrix A and coefficient matrix C. In each case

    either prove the statement or give an example showing that it is false.

    • If there is more than one solution, A has a row of zeros.
    • If A has a row of zeros, there is more than one solution.
    • If there is no solution, the row-echelon form of C has a row of zeros. • If the row-echelon form of C has a row of zeros there is no solution.

    Recall: The coefficient matrix C of a system of linear equations is the matrix obtained from the augmented matrix of the system by deleting its last column.

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