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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}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right] B = \left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right] C = \left[\begin{matrix}-6 & 8 & 1\end{matrix}\right] D = \left[\begin{matrix}7 & 1 & 4\\6 & 0 & 5\\6 & 7 & -8\end{matrix}\right] E = \left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right] \end{equation*}
\begin{question}Use the matrices below to answer the following questions:
\begin{equation*}A = \left[\begin{matrix}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right] B = \left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right] C = \left[\begin{matrix}-6 & 8 & 1\end{matrix}\right] D = \left[\begin{matrix}7 & 1 & 4\\6 & 0 & 5\\6 & 7 & -8\end{matrix}\right] E = \left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right] \end{equation*}
\begin{enumerate}
\item (10pts) Find $A + E$ and $C + D$
\soln{9cm}{
$\left[\begin{matrix}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right]+\left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right]=\left[\begin{matrix}-8 & 21 & -33\\21 & 29 & 12\end{matrix}\right]$ The sum is undefined. The matricies do not have the same shape.
}
\item (10pts) Find $BC$ and $CB$
\soln{9cm}{
The product is undefined. $\left[\begin{matrix}-6 & 8 & 1\end{matrix}\right]\left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right]=\left[\begin{matrix}-96 & -74\end{matrix}\right]$
}
\item (10pts) Find the inverse of Matrix D, that is $D^{-1}$
\soln{9cm}{
$\left[\begin{matrix}-35 & 36 & 5\\78 & -80 & -11\\42 & -43 & -6\end{matrix}\right]$
}
\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}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right] B = \left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right] C = \left[\begin{matrix}-6 & 8 & 1\end{matrix}\right] D = \left[\begin{matrix}7 & 1 & 4\\6 & 0 & 5\\6 & 7 & -8\end{matrix}\right] E = \left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right] " src="/equation_images/%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-6%20%26%2019%20%26%20-14%5C%5C6%20%26%2012%20%26%2010%5Cend%7Bmatrix%7D%5Cright%5D%20B%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D12%20%26%202%5C%5C-2%20%26%20-8%5C%5C-8%20%26%202%5Cend%7Bmatrix%7D%5Cright%5D%20C%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-6%20%26%208%20%26%201%5Cend%7Bmatrix%7D%5Cright%5D%20D%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D7%20%26%201%20%26%204%5C%5C6%20%26%200%20%26%205%5C%5C6%20%26%207%20%26%20-8%5Cend%7Bmatrix%7D%5Cright%5D%20E%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-2%20%26%202%20%26%20-19%5C%5C15%20%26%2017%20%26%202%5Cend%7Bmatrix%7D%5Cright%5D%20%20" alt="LaTeX: A = \left[\begin{matrix}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right] B = \left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right] C = \left[\begin{matrix}-6 & 8 & 1\end{matrix}\right] D = \left[\begin{matrix}7 & 1 & 4\\6 & 0 & 5\\6 & 7 & -8\end{matrix}\right] E = \left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right] " data-equation-content=" A = \left[\begin{matrix}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right] B = \left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right] C = \left[\begin{matrix}-6 & 8 & 1\end{matrix}\right] D = \left[\begin{matrix}7 & 1 & 4\\6 & 0 & 5\\6 & 7 & -8\end{matrix}\right] E = \left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\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}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right]+\left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right]=\left[\begin{matrix}-8 & 21 & -33\\21 & 29 & 12\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-6%20%26%2019%20%26%20-14%5C%5C6%20%26%2012%20%26%2010%5Cend%7Bmatrix%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Bmatrix%7D-2%20%26%202%20%26%20-19%5C%5C15%20%26%2017%20%26%202%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D-8%20%26%2021%20%26%20-33%5C%5C21%20%26%2029%20%26%2012%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right]+\left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right]=\left[\begin{matrix}-8 & 21 & -33\\21 & 29 & 12\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-6 & 19 & -14\\6 & 12 & 10\end{matrix}\right]+\left[\begin{matrix}-2 & 2 & -19\\15 & 17 & 2\end{matrix}\right]=\left[\begin{matrix}-8 & 21 & -33\\21 & 29 & 12\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}-6 & 8 & 1\end{matrix}\right]\left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right]=\left[\begin{matrix}-96 & -74\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-6%20%26%208%20%26%201%5Cend%7Bmatrix%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Bmatrix%7D12%20%26%202%5C%5C-2%20%26%20-8%5C%5C-8%20%26%202%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D-96%20%26%20-74%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-6 & 8 & 1\end{matrix}\right]\left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right]=\left[\begin{matrix}-96 & -74\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-6 & 8 & 1\end{matrix}\right]\left[\begin{matrix}12 & 2\\-2 & -8\\-8 & 2\end{matrix}\right]=\left[\begin{matrix}-96 & -74\end{matrix}\right] " /> </li>
<li> <img class="equation_image" title=" \displaystyle \left[\begin{matrix}-35 & 36 & 5\\78 & -80 & -11\\42 & -43 & -6\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-35%20%26%2036%20%26%205%5C%5C78%20%26%20-80%20%26%20-11%5C%5C42%20%26%20-43%20%26%20-6%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-35 & 36 & 5\\78 & -80 & -11\\42 & -43 & -6\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-35 & 36 & 5\\78 & -80 & -11\\42 & -43 & -6\end{matrix}\right] " /> </li>
</ol></p> </p>