Chapter 11, Problem 7CT

To determine

To find: The matrix $2A+C$ .

Answer to Problem 7CT

The matrix $2A+C$ is $\left[\begin{array}{cc}6& 4\\ 1& -11\\ 5& 12\end{array}\right]$ .

Explanation of Solution

Given information:

The matrix A is

  $A=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& 2\end{array}\right]$

The matrix B is

  $B=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right]$

The matrix C is

  $C=\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right]$

Calculation:

The relation between the matrices is

  $2A+C$

Substitute the values in the above relation.

  $\begin{array}{c}2A+C=2\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& 2\end{array}\right]+\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right]\\ =\left[\begin{array}{cc}2& -2\\ 0& -8\\ 6& 4\end{array}\right]+\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right]\\ =\left[\begin{array}{cc}2+4& \left(-2\right)+6\\ 0+1& \left(-8\right)+\left(-3\right)\\ 6+\left(-1\right)& 4+8\end{array}\right]\\ =\left[\begin{array}{cc}6& 4\\ 1& -11\\ 5& 12\end{array}\right]\end{array}$

Therefore, the matrix $2A+C$ is $\left[\begin{array}{cc}6& 4\\ 1& -11\\ 5& 12\end{array}\right]$ .