Chapter 6.3, Problem 1CB

To determine

Tocalculate : Solve the system using an augmented Matrix.

Answer to Problem 1CB

  $\begin{array}{l}x=12\\ y=-5\end{array}$

Explanation of Solution

Given information :

  $3x+2y=26$

  $x+y=7$

Here the coefficient matrix is $\left[\begin{array}{cc}3& 2\\ 1& 1\end{array}\right]$ and the augmented matrix is $[\begin{array}{cc}3& 2\\ 1& 1\end{array}|\begin{array}{c}26\\ 7\end{array}]$

Calculation: We use the given system of equations

First of all convert the system of equations in augmented matrix.

We get, $[\begin{array}{cc}3& 2\\ 1& 1\end{array}|\begin{array}{c}26\\ 7\end{array}]$

Now apply the row or column operations on it

  $$

  $[\begin{array}{cc}3& 2\\ 1& 1\end{array}|\begin{array}{c}26\\ 7\end{array}]$

  $R1\to R1-2R2$

We get,

  $$

  $[\begin{array}{cc}1& 0\\ 1& 1\end{array}|\begin{array}{c}12\\ 7\end{array}]$

  $R2\to R2-R1$

We get,

  $[\begin{array}{cc}1& 0\\ 0& 1\end{array}|\begin{array}{c}12\\ -5\end{array}]$

This is augmented matrix in form $\left[Ab\right]$

  $\Rightarrow x=12$

  $y=-5$