Chapter 4.2, Problem 37HP

To determine

To find: The elements of $C$ .

Answer to Problem 37HP

The value of $C=\left[\begin{array}{cc}7& 5\\ -1& -5\end{array}\right]$ .

Explanation of Solution

Given:

The matrix $A$ is $A=\left[\begin{array}{cc}-3& -4\\ 8& 6\end{array}\right]$ and $B=\left[\begin{array}{cc}5& -1\\ 2& -4\end{array}\right]$ .

The given equation is $3A-4B+6C=\left[\begin{array}{cc}13& 22\\ 10& 4\end{array}\right]$

Calculation:

Consider the given matrix equation is,

  $3A-4B+6C=\left[\begin{array}{cc}13& 22\\ 10& 4\end{array}\right]$

Then,

  $\begin{array}{l}3\left[\begin{array}{cc}-3& -4\\ 8& 6\end{array}\right]-4\left[\begin{array}{cc}5& -1\\ 2& -4\end{array}\right]+6C=\left[\begin{array}{cc}13& 22\\ 10& 4\end{array}\right]\\ \left[\begin{array}{cc}-9& -12\\ 24& 18\end{array}\right]-4\left[\begin{array}{cc}20& -4\\ 8& -16\end{array}\right]+6C=\left[\begin{array}{cc}13& 22\\ 10& 4\end{array}\right]\\ \left[\begin{array}{cc}-29& -8\\ 16& 34\end{array}\right]+6C=\left[\begin{array}{cc}13& 22\\ 10& 4\end{array}\right]\\ 6C=\left[\begin{array}{cc}13& 22\\ 10& 4\end{array}\right]-\left[\begin{array}{cc}-29& -8\\ 16& 34\end{array}\right]\end{array}$

Solve further as,

  $\begin{array}{l}6C=\left[\begin{array}{cc}42& 30\\ -6& -30\end{array}\right]\\ C=\left[\begin{array}{cc}7& 5\\ -1& -5\end{array}\right]\end{array}$