Chapter 7.4, Problem 19E

To determine

To calculate: To write the given system of equations in augmented form.

Answer to Problem 19E

  $\left[\begin{array}{cccc}7& -5& 1& 13\\ 19& 0& -8& 10\end{array}\right]$

Explanation of Solution

Given information: The given system of equations is,

  $\{\begin{array}{c}7x-5y+z=13\\ 19x-8z=10\end{array}$

Calculation: The given system of equations is,

  $\{\begin{array}{c}7x-5y+z=13\\ 19x-8z=10\end{array}$

Rewrite the above system of equations in such a way that all the variables x, y and z have their coefficients.

That is,

  $\{\begin{array}{c}7x-5y+z=13\\ 19x+0y-8z=10\end{array}$

There are two rows and three variables therefore, the matrix has dimension $2\times 3$ .

The augmented matrix therefore has dimension $2\times 4$ .

Write the coefficients of x in first column, coefficients of y in second column and coefficients of z in third column and the constants in fourth column.

Finally, separate the coefficients with the constants with a dotted line.

Hence, the augmented matrix is,

  $\left[\begin{array}{cccc}7& -5& 1& 13\\ 19& 0& -8& 10\end{array}\right]$