Chapter 4.6, Problem 38HP

To determine

To evaluate: among Cody and Megan who have opt correct format for writing matrix equations.

Answer to Problem 38HP

Megan is correct.

Explanation of Solution

Given information:

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

Formula used:

Matrices can be used to represent and solve system of equations. Write the left side of f the matrix equation as the product of the coefficient matrix and the variable matrix. Write the right side as a constant matrix.

Calculation:

Consider the matrix equations for the system,

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

The matrix equations can be written as :-

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

According to this, Megan has written the matrix correct whereas Cody has mistaken in writing the matrix. Cody put 3 for x in the second equation instead of 4.

Hence, Megan is correct.