Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}-18 & 13\\-5 & -5\\19 & -9\end{matrix}\right] B = \left[\begin{matrix}-20 & -20 & 11\\-4 & -19 & 14\end{matrix}\right] C = \left[\begin{matrix}12 & -2\end{matrix}\right] D = \left[\begin{matrix}5 & 3 & 0\\-7 & -8 & 6\\-3 & -5 & 5\end{matrix}\right] E = \left[\begin{matrix}-9 & -20\\19 & 7\\-8 & 11\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}-18 & 13\\-5 & -5\\19 & -9\end{matrix}\right]+\left[\begin{matrix}-9 & -20\\19 & 7\\-8 & 11\end{matrix}\right]=\left[\begin{matrix}-27 & -7\\14 & 2\\11 & 2\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}12 & -2\end{matrix}\right]\left[\begin{matrix}-20 & -20 & 11\\-4 & -19 & 14\end{matrix}\right]=\left[\begin{matrix}-232 & -202 & 104\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}-10 & -15 & 18\\17 & 25 & -30\\11 & 16 & -19\end{matrix}\right]