Chapter 2.1, Problem 86E

True or False In Exercises 85 and 86, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriaste statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) If $A$ is a $m\times n$ matrix and $B$ is a $n\times r$ matrix, then the product $AB$ is an $m\times r$ matrix.

(b) The matrix equation $A\mathbf{x}=\mathbf{b}$ where $A$ is the coefficient matrix and $\mathbf{x}$ and $\mathbf{b}$ are column matrices, can be used to represent a system of linear equations.