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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}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right] B = \left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right] C = \left[\begin{matrix}-19 & 1 & 17\end{matrix}\right] D = \left[\begin{matrix}-1 & 9 & -2\\5 & -4 & 2\\9 & 6 & 1\end{matrix}\right] E = \left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right] \end{equation*}
\begin{question}Use the matrices below to answer the following questions:
\begin{equation*}A = \left[\begin{matrix}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right] B = \left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right] C = \left[\begin{matrix}-19 & 1 & 17\end{matrix}\right] D = \left[\begin{matrix}-1 & 9 & -2\\5 & -4 & 2\\9 & 6 & 1\end{matrix}\right] E = \left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right] \end{equation*}
\begin{enumerate}
\item (10pts) Find $A + E$ and $C + D$
\soln{9cm}{
$\left[\begin{matrix}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right]+\left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right]=\left[\begin{matrix}5 & -29 & 13\\11 & -7 & 2\end{matrix}\right]$ The sum is undefined. The matricies do not have the same shape.
}
\item (10pts) Find $BC$ and $CB$
\soln{9cm}{
The product is undefined. $\left[\begin{matrix}-19 & 1 & 17\end{matrix}\right]\left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right]=\left[\begin{matrix}-172 & -182\end{matrix}\right]$
}
\item (10pts) Find the inverse of Matrix D, that is $D^{-1}$
\soln{9cm}{
$\left[\begin{matrix}-16 & -21 & 10\\13 & 17 & -8\\66 & 87 & -41\end{matrix}\right]$
}
\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}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right] B = \left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right] C = \left[\begin{matrix}-19 & 1 & 17\end{matrix}\right] D = \left[\begin{matrix}-1 & 9 & -2\\5 & -4 & 2\\9 & 6 & 1\end{matrix}\right] E = \left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right] " src="/equation_images/%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D11%20%26%20-14%20%26%205%5C%5C-2%20%26%20-10%20%26%20-12%5Cend%7Bmatrix%7D%5Cright%5D%20B%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D17%20%26%2013%5C%5C-2%20%26%2014%5C%5C9%20%26%203%5Cend%7Bmatrix%7D%5Cright%5D%20C%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-19%20%26%201%20%26%2017%5Cend%7Bmatrix%7D%5Cright%5D%20D%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-1%20%26%209%20%26%20-2%5C%5C5%20%26%20-4%20%26%202%5C%5C9%20%26%206%20%26%201%5Cend%7Bmatrix%7D%5Cright%5D%20E%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-6%20%26%20-15%20%26%208%5C%5C13%20%26%203%20%26%2014%5Cend%7Bmatrix%7D%5Cright%5D%20%20" alt="LaTeX: A = \left[\begin{matrix}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right] B = \left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right] C = \left[\begin{matrix}-19 & 1 & 17\end{matrix}\right] D = \left[\begin{matrix}-1 & 9 & -2\\5 & -4 & 2\\9 & 6 & 1\end{matrix}\right] E = \left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right] " data-equation-content=" A = \left[\begin{matrix}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right] B = \left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right] C = \left[\begin{matrix}-19 & 1 & 17\end{matrix}\right] D = \left[\begin{matrix}-1 & 9 & -2\\5 & -4 & 2\\9 & 6 & 1\end{matrix}\right] E = \left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\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}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right]+\left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right]=\left[\begin{matrix}5 & -29 & 13\\11 & -7 & 2\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D11%20%26%20-14%20%26%205%5C%5C-2%20%26%20-10%20%26%20-12%5Cend%7Bmatrix%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Bmatrix%7D-6%20%26%20-15%20%26%208%5C%5C13%20%26%203%20%26%2014%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D5%20%26%20-29%20%26%2013%5C%5C11%20%26%20-7%20%26%202%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right]+\left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right]=\left[\begin{matrix}5 & -29 & 13\\11 & -7 & 2\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}11 & -14 & 5\\-2 & -10 & -12\end{matrix}\right]+\left[\begin{matrix}-6 & -15 & 8\\13 & 3 & 14\end{matrix}\right]=\left[\begin{matrix}5 & -29 & 13\\11 & -7 & 2\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}-19 & 1 & 17\end{matrix}\right]\left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right]=\left[\begin{matrix}-172 & -182\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-19%20%26%201%20%26%2017%5Cend%7Bmatrix%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Bmatrix%7D17%20%26%2013%5C%5C-2%20%26%2014%5C%5C9%20%26%203%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D-172%20%26%20-182%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-19 & 1 & 17\end{matrix}\right]\left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right]=\left[\begin{matrix}-172 & -182\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-19 & 1 & 17\end{matrix}\right]\left[\begin{matrix}17 & 13\\-2 & 14\\9 & 3\end{matrix}\right]=\left[\begin{matrix}-172 & -182\end{matrix}\right] " /> </li>
<li> <img class="equation_image" title=" \displaystyle \left[\begin{matrix}-16 & -21 & 10\\13 & 17 & -8\\66 & 87 & -41\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-16%20%26%20-21%20%26%2010%5C%5C13%20%26%2017%20%26%20-8%5C%5C66%20%26%2087%20%26%20-41%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-16 & -21 & 10\\13 & 17 & -8\\66 & 87 & -41\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-16 & -21 & 10\\13 & 17 & -8\\66 & 87 & -41\end{matrix}\right] " /> </li>
</ol></p> </p>