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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}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right] B = \left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right] C = \left[\begin{matrix}1 & -20\end{matrix}\right] D = \left[\begin{matrix}-5 & 4 & -6\\0 & -4 & -3\\4 & 1 & 8\end{matrix}\right] E = \left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right] \end{equation*}
\begin{question}Use the matrices below to answer the following questions:
\begin{equation*}A = \left[\begin{matrix}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right] B = \left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right] C = \left[\begin{matrix}1 & -20\end{matrix}\right] D = \left[\begin{matrix}-5 & 4 & -6\\0 & -4 & -3\\4 & 1 & 8\end{matrix}\right] E = \left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right] \end{equation*}
\begin{enumerate}
\item (10pts) Find $A + E$ and $C + D$
\soln{9cm}{
$\left[\begin{matrix}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right]+\left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right]=\left[\begin{matrix}-14 & -2\\-10 & -11\\-13 & -5\end{matrix}\right]$ The sum is undefined. The matricies do not have the same shape.
}
\item (10pts) Find $BC$ and $CB$
\soln{9cm}{
The product is undefined. $\left[\begin{matrix}1 & -20\end{matrix}\right]\left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right]=\left[\begin{matrix}27 & -92 & 300\end{matrix}\right]$
}
\item (10pts) Find the inverse of Matrix D, that is $D^{-1}$
\soln{9cm}{
$\left[\begin{matrix}-29 & -38 & -36\\-12 & -16 & -15\\16 & 21 & 20\end{matrix}\right]$
}
\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}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right] B = \left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right] C = \left[\begin{matrix}1 & -20\end{matrix}\right] D = \left[\begin{matrix}-5 & 4 & -6\\0 & -4 & -3\\4 & 1 & 8\end{matrix}\right] E = \left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right] " src="/equation_images/%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-20%20%26%2011%5C%5C-3%20%26%20-20%5C%5C-2%20%26%206%5Cend%7Bmatrix%7D%5Cright%5D%20B%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D7%20%26%208%20%26%200%5C%5C-1%20%26%205%20%26%20-15%5Cend%7Bmatrix%7D%5Cright%5D%20C%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%20-20%5Cend%7Bmatrix%7D%5Cright%5D%20D%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-5%20%26%204%20%26%20-6%5C%5C0%20%26%20-4%20%26%20-3%5C%5C4%20%26%201%20%26%208%5Cend%7Bmatrix%7D%5Cright%5D%20E%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D6%20%26%20-13%5C%5C-7%20%26%209%5C%5C-11%20%26%20-11%5Cend%7Bmatrix%7D%5Cright%5D%20%20" alt="LaTeX: A = \left[\begin{matrix}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right] B = \left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right] C = \left[\begin{matrix}1 & -20\end{matrix}\right] D = \left[\begin{matrix}-5 & 4 & -6\\0 & -4 & -3\\4 & 1 & 8\end{matrix}\right] E = \left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right] " data-equation-content=" A = \left[\begin{matrix}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right] B = \left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right] C = \left[\begin{matrix}1 & -20\end{matrix}\right] D = \left[\begin{matrix}-5 & 4 & -6\\0 & -4 & -3\\4 & 1 & 8\end{matrix}\right] E = \left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -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}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right]+\left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right]=\left[\begin{matrix}-14 & -2\\-10 & -11\\-13 & -5\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-20%20%26%2011%5C%5C-3%20%26%20-20%5C%5C-2%20%26%206%5Cend%7Bmatrix%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Bmatrix%7D6%20%26%20-13%5C%5C-7%20%26%209%5C%5C-11%20%26%20-11%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D-14%20%26%20-2%5C%5C-10%20%26%20-11%5C%5C-13%20%26%20-5%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right]+\left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right]=\left[\begin{matrix}-14 & -2\\-10 & -11\\-13 & -5\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-20 & 11\\-3 & -20\\-2 & 6\end{matrix}\right]+\left[\begin{matrix}6 & -13\\-7 & 9\\-11 & -11\end{matrix}\right]=\left[\begin{matrix}-14 & -2\\-10 & -11\\-13 & -5\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}1 & -20\end{matrix}\right]\left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right]=\left[\begin{matrix}27 & -92 & 300\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%20-20%5Cend%7Bmatrix%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Bmatrix%7D7%20%26%208%20%26%200%5C%5C-1%20%26%205%20%26%20-15%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D27%20%26%20-92%20%26%20300%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & -20\end{matrix}\right]\left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right]=\left[\begin{matrix}27 & -92 & 300\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & -20\end{matrix}\right]\left[\begin{matrix}7 & 8 & 0\\-1 & 5 & -15\end{matrix}\right]=\left[\begin{matrix}27 & -92 & 300\end{matrix}\right] " /> </li>
<li> <img class="equation_image" title=" \displaystyle \left[\begin{matrix}-29 & -38 & -36\\-12 & -16 & -15\\16 & 21 & 20\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-29%20%26%20-38%20%26%20-36%5C%5C-12%20%26%20-16%20%26%20-15%5C%5C16%20%26%2021%20%26%2020%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-29 & -38 & -36\\-12 & -16 & -15\\16 & 21 & 20\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-29 & -38 & -36\\-12 & -16 & -15\\16 & 21 & 20\end{matrix}\right] " /> </li>
</ol></p> </p>