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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}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right] B = \left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right] C = \left[\begin{matrix}11 & -16\end{matrix}\right] D = \left[\begin{matrix}-1 & -2 & 3\\-1 & -3 & 3\\1 & 8 & -2\end{matrix}\right] E = \left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right] \end{equation*}
\begin{question}Use the matrices below to answer the following questions:
\begin{equation*}A = \left[\begin{matrix}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right] B = \left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right] C = \left[\begin{matrix}11 & -16\end{matrix}\right] D = \left[\begin{matrix}-1 & -2 & 3\\-1 & -3 & 3\\1 & 8 & -2\end{matrix}\right] E = \left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right] \end{equation*}
\begin{enumerate}
\item (10pts) Find $A + E$ and $C + D$
\soln{9cm}{
$\left[\begin{matrix}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right]+\left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right]=\left[\begin{matrix}-12 & -15\\-15 & 33\\10 & 10\end{matrix}\right]$ The sum is undefined. The matricies do not have the same shape.
}
\item (10pts) Find $BC$ and $CB$
\soln{9cm}{
The product is undefined. $\left[\begin{matrix}11 & -16\end{matrix}\right]\left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right]=\left[\begin{matrix}-45 & -208 & 481\end{matrix}\right]$
}
\item (10pts) Find the inverse of Matrix D, that is $D^{-1}$
\soln{9cm}{
$\left[\begin{matrix}-18 & 20 & 3\\1 & -1 & 0\\-5 & 6 & 1\end{matrix}\right]$
}
\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}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right] B = \left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right] C = \left[\begin{matrix}11 & -16\end{matrix}\right] D = \left[\begin{matrix}-1 & -2 & 3\\-1 & -3 & 3\\1 & 8 & -2\end{matrix}\right] E = \left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right] " src="/equation_images/%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-4%20%26%20-8%5C%5C-6%20%26%2018%5C%5C-5%20%26%2015%5Cend%7Bmatrix%7D%5Cright%5D%20B%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-7%20%26%200%20%26%2019%5C%5C-2%20%26%2013%20%26%20-17%5Cend%7Bmatrix%7D%5Cright%5D%20C%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D11%20%26%20-16%5Cend%7Bmatrix%7D%5Cright%5D%20D%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-1%20%26%20-2%20%26%203%5C%5C-1%20%26%20-3%20%26%203%5C%5C1%20%26%208%20%26%20-2%5Cend%7Bmatrix%7D%5Cright%5D%20E%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-8%20%26%20-7%5C%5C-9%20%26%2015%5C%5C15%20%26%20-5%5Cend%7Bmatrix%7D%5Cright%5D%20%20" alt="LaTeX: A = \left[\begin{matrix}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right] B = \left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right] C = \left[\begin{matrix}11 & -16\end{matrix}\right] D = \left[\begin{matrix}-1 & -2 & 3\\-1 & -3 & 3\\1 & 8 & -2\end{matrix}\right] E = \left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right] " data-equation-content=" A = \left[\begin{matrix}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right] B = \left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right] C = \left[\begin{matrix}11 & -16\end{matrix}\right] D = \left[\begin{matrix}-1 & -2 & 3\\-1 & -3 & 3\\1 & 8 & -2\end{matrix}\right] E = \left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\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}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right]+\left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right]=\left[\begin{matrix}-12 & -15\\-15 & 33\\10 & 10\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-4%20%26%20-8%5C%5C-6%20%26%2018%5C%5C-5%20%26%2015%5Cend%7Bmatrix%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Bmatrix%7D-8%20%26%20-7%5C%5C-9%20%26%2015%5C%5C15%20%26%20-5%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D-12%20%26%20-15%5C%5C-15%20%26%2033%5C%5C10%20%26%2010%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right]+\left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right]=\left[\begin{matrix}-12 & -15\\-15 & 33\\10 & 10\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-4 & -8\\-6 & 18\\-5 & 15\end{matrix}\right]+\left[\begin{matrix}-8 & -7\\-9 & 15\\15 & -5\end{matrix}\right]=\left[\begin{matrix}-12 & -15\\-15 & 33\\10 & 10\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}11 & -16\end{matrix}\right]\left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right]=\left[\begin{matrix}-45 & -208 & 481\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D11%20%26%20-16%5Cend%7Bmatrix%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Bmatrix%7D-7%20%26%200%20%26%2019%5C%5C-2%20%26%2013%20%26%20-17%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D-45%20%26%20-208%20%26%20481%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}11 & -16\end{matrix}\right]\left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right]=\left[\begin{matrix}-45 & -208 & 481\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}11 & -16\end{matrix}\right]\left[\begin{matrix}-7 & 0 & 19\\-2 & 13 & -17\end{matrix}\right]=\left[\begin{matrix}-45 & -208 & 481\end{matrix}\right] " /> </li>
<li> <img class="equation_image" title=" \displaystyle \left[\begin{matrix}-18 & 20 & 3\\1 & -1 & 0\\-5 & 6 & 1\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-18%20%26%2020%20%26%203%5C%5C1%20%26%20-1%20%26%200%5C%5C-5%20%26%206%20%26%201%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-18 & 20 & 3\\1 & -1 & 0\\-5 & 6 & 1\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-18 & 20 & 3\\1 & -1 & 0\\-5 & 6 & 1\end{matrix}\right] " /> </li>
</ol></p> </p>