Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}20 & -8 & -14\\8 & -19 & 20\end{matrix}\right] B = \left[\begin{matrix}19 & 3\\-5 & 20\\18 & 4\end{matrix}\right] C = \left[\begin{matrix}2 & 16 & 1\end{matrix}\right] D = \left[\begin{matrix}2 & -4 & -5\\0 & 1 & -1\\-1 & -3 & 8\end{matrix}\right] E = \left[\begin{matrix}12 & -20 & 4\\9 & 13 & 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}20 & -8 & -14\\8 & -19 & 20\end{matrix}\right]+\left[\begin{matrix}12 & -20 & 4\\9 & 13 & 8\end{matrix}\right]=\left[\begin{matrix}32 & -28 & -10\\17 & -6 & 28\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}2 & 16 & 1\end{matrix}\right]\left[\begin{matrix}19 & 3\\-5 & 20\\18 & 4\end{matrix}\right]=\left[\begin{matrix}-24 & 330\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}5 & 47 & 9\\1 & 11 & 2\\1 & 10 & 2\end{matrix}\right]