Question

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

An augmented matrix consists of the coefficients and the constant terms of a system of equations.

Short answer

The given statement is true.

Step-by-step solution

Step 1. State the concept of augmented matrix.

Elements of matrix is a set of simultaneous linear equations consisting of the coefficients with the constant terms, is augmented matrix.

Step 2. Explanation of the statement.

To write the equations in augmented matrix place the coefficients of the equations and the constant terms into a matrix separated by a dashed line.

Here, an example of augmented matrix:

$\left[\begin{array}{ccc}1& -1& 5\\ 3& 3& 3\end{array}\right]$

Step 3. Write whether the statement is true or false.

Since, the row of the augmented matrix represents constant terms and the column of the augmented matrix represents coefficients terms of variable.

Hence, the given statement “An augmented matrix consists of the coefficients and the constant terms of a system of equations.” is true.