Directions:

1. Write your name with one character in each box below.
2. Show all work. No credit for answers without work.

1. [4 parts, 1 point each] Compute the following matrices if defined.

   $$\begin{array}{llllllllllllllll}\hfill A& =\left[\begin{array}{cc}\hfill 1& \hfill -1\\ \hfill 2& \hfill 4\end{array}\right]& \hfill B& =\left[\begin{array}{cc}\hfill 2& \hfill 0\\ \hfill 0& \hfill 3\\ \hfill 1& \hfill -3\end{array}\right]& \hfill C& =\left[\begin{array}{cc}\hfill 3& \hfill -2\\ \hfill 1& \hfill 5\end{array}\right]& \hfill D& =\left[\begin{array}{ccc}\hfill -1& \hfill 2& \hfill 5\end{array}\right]& \hfill & & \hfill & & \hfill & & \hfill & \end{array}$$
   1. $A+2C$
       

   2. $\mathit{𝐵𝐶}$
       

      auto

   3. $D{D}^T$
       
   4. $D^{T}D$
       

2. [6 points] Solve the following system.

   $$\begin{array}{ccccccc}\hfill -3x_1& \hfill +& \hfill 4x_2& \hfill -& \hfill 4x_3& \hfill =& \hfill 1\\ \hfill -11x_1& \hfill +& \hfill 16x_2& \hfill -& \hfill 15x_3& \hfill =& \hfill 2\\ \hfill -x_1& \hfill +& \hfill x_2& \hfill -& \hfill x_3& \hfill =& \hfill 3\end{array}$$