Chapter 3.6, Problem 40PPSE

Solution

To state: Your classmates error and explain how to correct it if the solution is $x=2,y=0$ and the matrix written by your classmate is shown below that represents a system.

  $\left[\begin{array}{ccc}\begin{array}{l}1\\ 0\end{array}& \begin{array}{l}0\\ 0\end{array}& \begin{array}{l}2\\ 0\end{array}\end{array}\right]$

The correct matrix should be $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}|\begin{array}{c}2\\ 0\end{array}\right]$ .

Given information:

The given solution of the system is $x=2,y=0$ .

Explanation:

Consider the matrix:

  $\left[\begin{array}{ccc}\begin{array}{l}1\\ 0\end{array}& \begin{array}{l}0\\ 0\end{array}& \begin{array}{l}2\\ 0\end{array}\end{array}\right]$

The matrix representation of the above matrix with solution $x=2,y=0$ :

  $\begin{array}{c}x+0y=2\\ 0x+0y=0\end{array}$

After simplifying the above system the resultant value of x will be 2.

Thus the matrix $\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}|\begin{array}{c}2\\ 0\end{array}\right]$ represents a system whose solution is $x=2$ .

But it is given that the solution for the matrix is $x=2,y=0$ .

Therefore, the correct matrix should be $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}|\begin{array}{c}2\\ 0\end{array}\right]$ whose solution is $x=2,y=0$ .