Let a be an mxn matrix. consider the statement. "for each b in rm, the equation ax b has a solution." because of a fundamental theorem about such matrix equations, this statement is equivalent to what other statements? choose all that apply. a. the rows of a span rn. b. each b in rm is a linear combination of the columns of a c. the columns of a span r d. the matrix a has a pivot position in each column. e. the matrix a has a pivot position in each row.

 The correct answer is :  B. Each b in Rm is a linear combination of the columns of A

C. The columns of A span R

 E. The matrix A has a pivot position in each row.

Step-by-step explanation:   These conditions correspond to Theorem 4: A square matrix A is invertible, yes and only if the det A ≠ 0

1. If the matrix is not full range, there are infinite solutions

2. Each row must have at least one pivot so that it has a solution

3. When a row is not linearly independent, the matrix is not full range and its determinant is zero.

4. For each b in Rm the equation Ax = b has a solution