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Questions: Algebra BusinessCalculus
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Use the matrices below to answer the following questions: \begin{equation*}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] \end{equation*}
\begin{question}Use the matrices below to answer the following questions:
\begin{equation*}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] \end{equation*}
\begin{enumerate}
\item (10pts) Find $A + E$ and $C + D$
\soln{9cm}{
$\left[\begin{matrix}-12 & -7\\15 & 3\\-19 & -18\end{matrix}\right]+\left[\begin{matrix}-15 & 18\\10 & 7\\-1 & 11\end{matrix}\right]=\left[\begin{matrix}-27 & 11\\25 & 10\\-20 & -7\end{matrix}\right]$ The sum is undefined. The matricies do not have the same shape.
}
\item (10pts) Find $BC$ and $CB$
\soln{9cm}{
The product is undefined. $\left[\begin{matrix}-18 & -10\end{matrix}\right]\left[\begin{matrix}-16 & 18 & 0\\15 & 11 & 4\end{matrix}\right]=\left[\begin{matrix}138 & -434 & -40\end{matrix}\right]$
}
\item (10pts) Find the inverse of Matrix D, that is $D^{-1}$
\soln{9cm}{
$\left[\begin{matrix}-27 & -55 & 61\\5 & 10 & -11\\-9 & -18 & 20\end{matrix}\right]$
}
\end{enumerate}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Use the matrices below to answer the following questions:
<img class="equation_image" title=" 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] " src="/equation_images/%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-12%20%26%20-7%5C%5C15%20%26%203%5C%5C-19%20%26%20-18%5Cend%7Bmatrix%7D%5Cright%5D%20B%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-16%20%26%2018%20%26%200%5C%5C15%20%26%2011%20%26%204%5Cend%7Bmatrix%7D%5Cright%5D%20C%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-18%20%26%20-10%5Cend%7Bmatrix%7D%5Cright%5D%20D%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D2%20%26%202%20%26%20-5%5C%5C-1%20%26%209%20%26%208%5C%5C0%20%26%209%20%26%205%5Cend%7Bmatrix%7D%5Cright%5D%20E%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-15%20%26%2018%5C%5C10%20%26%207%5C%5C-1%20%26%2011%5Cend%7Bmatrix%7D%5Cright%5D%20%20" alt="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] " data-equation-content=" 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] " />
<ol type="a">
<li>Find <img class="equation_image" title=" \displaystyle A + E " src="/equation_images/%20%5Cdisplaystyle%20A%20%2B%20E%20" alt="LaTeX: \displaystyle A + E " data-equation-content=" \displaystyle A + E " /> and <img class="equation_image" title=" \displaystyle C + D " src="/equation_images/%20%5Cdisplaystyle%20C%20%2B%20D%20" alt="LaTeX: \displaystyle C + D " data-equation-content=" \displaystyle C + D " /> </li>
<li>Find <img class="equation_image" title=" \displaystyle BC " src="/equation_images/%20%5Cdisplaystyle%20BC%20" alt="LaTeX: \displaystyle BC " data-equation-content=" \displaystyle BC " /> and <img class="equation_image" title=" \displaystyle CB " src="/equation_images/%20%5Cdisplaystyle%20CB%20" alt="LaTeX: \displaystyle CB " data-equation-content=" \displaystyle CB " /> </li>
<li>Find the inverse of Matrix D, that is <img class="equation_image" title=" \displaystyle D^{-1} " src="/equation_images/%20%5Cdisplaystyle%20D%5E%7B-1%7D%20" alt="LaTeX: \displaystyle D^{-1} " data-equation-content=" \displaystyle D^{-1} " /> </li>
</ol>
</p> </p><p> <p>
<ol type="a">
<li> <img class="equation_image" title=" \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] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-12%20%26%20-7%5C%5C15%20%26%203%5C%5C-19%20%26%20-18%5Cend%7Bmatrix%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Bmatrix%7D-15%20%26%2018%5C%5C10%20%26%207%5C%5C-1%20%26%2011%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D-27%20%26%2011%5C%5C25%20%26%2010%5C%5C-20%20%26%20-7%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="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] " data-equation-content=" \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.</li>
<li> The product is undefined. <img class="equation_image" title=" \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] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-18%20%26%20-10%5Cend%7Bmatrix%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Bmatrix%7D-16%20%26%2018%20%26%200%5C%5C15%20%26%2011%20%26%204%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D138%20%26%20-434%20%26%20-40%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="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] " data-equation-content=" \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] " /> </li>
<li> <img class="equation_image" title=" \displaystyle \left[\begin{matrix}-27 & -55 & 61\\5 & 10 & -11\\-9 & -18 & 20\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-27%20%26%20-55%20%26%2061%5C%5C5%20%26%2010%20%26%20-11%5C%5C-9%20%26%20-18%20%26%2020%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-27 & -55 & 61\\5 & 10 & -11\\-9 & -18 & 20\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-27 & -55 & 61\\5 & 10 & -11\\-9 & -18 & 20\end{matrix}\right] " /> </li>
</ol></p> </p>