Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right] B = \left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right] C = \left[\begin{matrix}7 & -2 & -17\end{matrix}\right] D = \left[\begin{matrix}7 & -4 & -7\\-3 & 1 & 4\\5 & -8 & 2\end{matrix}\right] E = \left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right]

  1. Find LaTeX: \displaystyle A + E and LaTeX: \displaystyle C + D
  2. Find LaTeX: \displaystyle BC and LaTeX: \displaystyle CB
  3. Find the inverse of Matrix D, that is LaTeX: \displaystyle D^{-1}

  1. LaTeX: \displaystyle \left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right]+\left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right]=\left[\begin{matrix}14 & 17 & -14\\-11 & -32 & -19\end{matrix}\right] The sum is undefined. The matricies do not have the same shape.
  2. The product is undefined. LaTeX: \displaystyle \left[\begin{matrix}7 & -2 & -17\end{matrix}\right]\left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right]=\left[\begin{matrix}385 & 307\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}34 & 64 & -9\\26 & 49 & -7\\19 & 36 & -5\end{matrix}\right]