Chapter 3.8, Problem 38HP

To determine

To find: The correct representation of given equations in matrix by two students.

Answer to Problem 38HP

Megan is correct! If we multiply the left side of the matrices, it gives the given equations.

Explanation of Solution

Given information: The equations are $5x+7y=19$ , $3y+4x=10$ and their matrix representation by

Cody is

  $\left[\begin{array}{cc}5& 7\\ 3& 4\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}19\\ 10\end{array}\right]$

and Megan is

  $\left[\begin{array}{cc}5& 7\\ 4& 3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}19\\ 10\end{array}\right]$

Calculation:

Let’s multiply left side matrices to get equations

For Cody,

  $\left[\begin{array}{cc}5& 7\\ 3& 4\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}19\\ 10\end{array}\right]$

Gives,

  $\begin{array}{l}5x+7y=19\\ 3x+4y=10\end{array}$

But multiply the Megan’s matrices

  $\left[\begin{array}{cc}5& 7\\ 4& 3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}19\\ 10\end{array}\right]$

It gives,

  $\begin{array}{l}5x+7y=19\\ 4x+3y=10\end{array}$

Rewrite the second equation as $3y+4x=10$

Megan’s equations are same as given equations.

Conclusion: Megan is correct!