Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}-12 & -7\\15 & 3\\-19 & -18\end{matrix}\right] B = \left[\begin{matrix}-16 & 18 & 0\\15 & 11 & 4\end{matrix}\right] C = \left[\begin{matrix}-18 & -10\end{matrix}\right] D = \left[\begin{matrix}2 & 2 & -5\\-1 & 9 & 8\\0 & 9 & 5\end{matrix}\right] E = \left[\begin{matrix}-15 & 18\\10 & 7\\-1 & 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}-12 & -7\\15 & 3\\-19 & -18\end{matrix}\right]+\left[\begin{matrix}-15 & 18\\10 & 7\\-1 & 11\end{matrix}\right]=\left[\begin{matrix}-27 & 11\\25 & 10\\-20 & -7\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}-18 & -10\end{matrix}\right]\left[\begin{matrix}-16 & 18 & 0\\15 & 11 & 4\end{matrix}\right]=\left[\begin{matrix}138 & -434 & -40\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}-27 & -55 & 61\\5 & 10 & -11\\-9 & -18 & 20\end{matrix}\right]