Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right] B = \left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right] C = \left[\begin{matrix}11 & -16\end{matrix}\right] D = \left[\begin{matrix}-1 & -2 & 3\\-1 & -3 & 3\\1 & 8 & -2\end{matrix}\right] E = \left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\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}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right]+\left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right]=\left[\begin{matrix}-12 & -15\\-15 & 33\\10 & 10\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}11 & -16\end{matrix}\right]\left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right]=\left[\begin{matrix}-45 & -208 & 481\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}-18 & 20 & 3\\1 & -1 & 0\\-5 & 6 & 1\end{matrix}\right]