Use the matrices below to answer the following questions: LaTeX: A = \left[\begin{matrix}-3 & 0\\-12 & 5\\14 & 3\end{matrix}\right] B = \left[\begin{matrix}-4 & -13 & -4\\3 & -12 & -15\end{matrix}\right] C = \left[\begin{matrix}15 & 7\end{matrix}\right] D = \left[\begin{matrix}7 & 8 & -7\\5 & 5 & 2\\-2 & -2 & -1\end{matrix}\right] E = \left[\begin{matrix}15 & -12\\3 & -18\\17 & 6\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}-3 & 0\\-12 & 5\\14 & 3\end{matrix}\right]+\left[\begin{matrix}15 & -12\\3 & -18\\17 & 6\end{matrix}\right]=\left[\begin{matrix}12 & -12\\-9 & -13\\31 & 9\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}15 & 7\end{matrix}\right]\left[\begin{matrix}-4 & -13 & -4\\3 & -12 & -15\end{matrix}\right]=\left[\begin{matrix}-39 & -279 & -165\end{matrix}\right]
  3. LaTeX: \displaystyle \left[\begin{matrix}-1 & 22 & 51\\1 & -21 & -49\\0 & -2 & -5\end{matrix}\right]