7. (10pt) Either prove the following statements, or give an example to show that it is false. (a) If a system of m linea
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7. (10pt) Either prove the following statements, or give an example to show that it is false. (a) If a system of m linea
solutions. (b) If a consistent system of m linear equations in n variables has coefficient matrix C (an m x n matrix) and augmented matrix A with m <n, then the system has infinitely many solutions. (c) If a system of m linear equations in n variables has coefficient matrix C (an mx n matrix) and augmented matrix A with the rank of A greater than the rank of C, then the system is inconsistent. (d) If a homogeneous system of m linear equations in n variables has coefficient matrix C (an m x n matrix) and mugmented matrix A where the rank of A is less than n, then the system has non-trivial solutions. (e) If a sequence of row operations is done to a consistent system of linear equations, then the resulting system is also consistent
7. (10pt) Either prove the following statements, or give an example to show that it is false. (a) If a system of m linear equations in n variables has coefficient matrix C (an m x n matrix) and augmented matrix A with m <n, then the system has infinitely many