Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}-16 & 16 & -16\\15 & -11 & 18\end{matrix}\right] B = \left[\begin{matrix}-20 & -1\\-13 & 17\\9 & -3\end{matrix}\right] C = \left[\begin{matrix}-6 & 6 & -1\end{matrix}\right] D = \left[\begin{matrix}4 & 0 & 1\\-8 & 7 & -1\\1 & 5 & 1\end{matrix}\right] E = \left[\begin{matrix}1 & -14 & -19\\-19 & -17 & -8\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}-16 & 16 & -16\\15 & -11 & 18\end{matrix}\right]+\left[\begin{matrix}1 & -14 & -19\\-19 & -17 & -8\end{matrix}\right]=\left[\begin{matrix}-15 & 2 & -35\\-4 & -28 & 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}-6 & 6 & -1\end{matrix}\right]\left[\begin{matrix}-20 & -1\\-13 & 17\\9 & -3\end{matrix}\right]=\left[\begin{matrix}33 & 111\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}12 & 5 & -7\\7 & 3 & -4\\-47 & -20 & 28\end{matrix}\right]