Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}-2 & -12\\16 & 17\\8 & -16\end{matrix}\right] B = \left[\begin{matrix}-9 & 5 & -20\\-11 & 4 & -11\end{matrix}\right] C = \left[\begin{matrix}18 & -7\end{matrix}\right] D = \left[\begin{matrix}-4 & 2 & -1\\9 & -4 & -2\\7 & -3 & -3\end{matrix}\right] E = \left[\begin{matrix}-20 & -17\\0 & 9\\20 & -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}-2 & -12\\16 & 17\\8 & -16\end{matrix}\right]+\left[\begin{matrix}-20 & -17\\0 & 9\\20 & -11\end{matrix}\right]=\left[\begin{matrix}-22 & -29\\16 & 26\\28 & -27\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 & -7\end{matrix}\right]\left[\begin{matrix}-9 & 5 & -20\\-11 & 4 & -11\end{matrix}\right]=\left[\begin{matrix}-85 & 62 & -283\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}6 & 9 & -8\\13 & 19 & -17\\1 & 2 & -2\end{matrix}\right]