Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}-14 & 19\\-17 & -4\\-19 & 19\end{matrix}\right] B = \left[\begin{matrix}-12 & -18 & -7\\-17 & 13 & 3\end{matrix}\right] C = \left[\begin{matrix}17 & -2\end{matrix}\right] D = \left[\begin{matrix}-3 & 2 & 6\\1 & 1 & 4\\-3 & -1 & -5\end{matrix}\right] E = \left[\begin{matrix}-4 & 14\\9 & 6\\-16 & -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}-14 & 19\\-17 & -4\\-19 & 19\end{matrix}\right]+\left[\begin{matrix}-4 & 14\\9 & 6\\-16 & -13\end{matrix}\right]=\left[\begin{matrix}-18 & 33\\-8 & 2\\-35 & 6\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}17 & -2\end{matrix}\right]\left[\begin{matrix}-12 & -18 & -7\\-17 & 13 & 3\end{matrix}\right]=\left[\begin{matrix}-170 & -332 & -125\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}-1 & 4 & 2\\-7 & 33 & 18\\2 & -9 & -5\end{matrix}\right]