Question

(1 point) Which of the following statements are true? Remember that a mathematical statement is said to be true it it is always true, uncer all circumstances.
A. Every matrix equation $A x=b$ corresponds to a vector equation with the same solution set.
B. If $A$ is an $m \times n$ matrix and if the equation $A x=b$ is inconsistent for some $b$ in $\mathrm{R}^{m+}$, then $A$ cannot have a pivot in every row.
C. The first entry in the product $A x$ is a sum of products.
D. If the augmented matrix $[A \mid b]$ has a pivot position in every row, then the equation $A x=b$ is inconsistent.
E. The equation $A x=b$ is consistent if the augmented matrix $[A \mid b]$ has a pivot position in every row.
F. If $A$ is an $m \times n$ matrix whose columns do not span $\mathbf{R}^m$, then the equation $A x=b$ is inconsistent for some $b$ in $\mathbf{R}^m$.