Question 1 • Let A be an m x n matrix. Choose the statement below that is not co

Question

Question 1 • Let A be an m x n matrix. Choose the statement below that is not correct. To make sure that A an equation Ax = b is consistent, verify that the last column of the augmented matrix (A b] is not a pivot column. B. an equation Ax = 0 has only the trivial solution, verify that there are no free variables. C. an equation Ax = b has a solution for any b in R", verify that the matrix A has a pivot position in every row. D. a vector b can be written as a linear combination of the columns of A, verify that Ax = b has a solution. E. a consistent system Ax = b has a unique solution, verify that the homogeneous system Ax = 0 has a nontrivial solution.

Explanation / Answer

Answer (c) is false statement

Reason

The system is inconsistent if [A b] has a pivot in the last ("b") column. The system is consistent if the matrix A has a pivot in every row.

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