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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}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right] B = \left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right] C = \left[\begin{matrix}7 & -2 & -17\end{matrix}\right] D = \left[\begin{matrix}7 & -4 & -7\\-3 & 1 & 4\\5 & -8 & 2\end{matrix}\right] E = \left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right] \end{equation*}
\begin{question}Use the matrices below to answer the following questions:
\begin{equation*}A = \left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right] B = \left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right] C = \left[\begin{matrix}7 & -2 & -17\end{matrix}\right] D = \left[\begin{matrix}7 & -4 & -7\\-3 & 1 & 4\\5 & -8 & 2\end{matrix}\right] E = \left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right] \end{equation*}
\begin{enumerate}
\item (10pts) Find $A + E$ and $C + D$
\soln{9cm}{
$\left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right]+\left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right]=\left[\begin{matrix}14 & 17 & -14\\-11 & -32 & -19\end{matrix}\right]$ The sum is undefined. The matricies do not have the same shape.
}
\item (10pts) Find $BC$ and $CB$
\soln{9cm}{
The product is undefined. $\left[\begin{matrix}7 & -2 & -17\end{matrix}\right]\left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right]=\left[\begin{matrix}385 & 307\end{matrix}\right]$
}
\item (10pts) Find the inverse of Matrix D, that is $D^{-1}$
\soln{9cm}{
$\left[\begin{matrix}34 & 64 & -9\\26 & 49 & -7\\19 & 36 & -5\end{matrix}\right]$
}
\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}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right] B = \left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right] C = \left[\begin{matrix}7 & -2 & -17\end{matrix}\right] D = \left[\begin{matrix}7 & -4 & -7\\-3 & 1 & 4\\5 & -8 & 2\end{matrix}\right] E = \left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right] " src="/equation_images/%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D13%20%26%2013%20%26%20-15%5C%5C-17%20%26%20-18%20%26%20-6%5Cend%7Bmatrix%7D%5Cright%5D%20B%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D3%20%26%200%5C%5C-12%20%26%20-9%5C%5C-20%20%26%20-17%5Cend%7Bmatrix%7D%5Cright%5D%20C%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D7%20%26%20-2%20%26%20-17%5Cend%7Bmatrix%7D%5Cright%5D%20D%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D7%20%26%20-4%20%26%20-7%5C%5C-3%20%26%201%20%26%204%5C%5C5%20%26%20-8%20%26%202%5Cend%7Bmatrix%7D%5Cright%5D%20E%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%204%20%26%201%5C%5C6%20%26%20-14%20%26%20-13%5Cend%7Bmatrix%7D%5Cright%5D%20%20" alt="LaTeX: A = \left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right] B = \left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right] C = \left[\begin{matrix}7 & -2 & -17\end{matrix}\right] D = \left[\begin{matrix}7 & -4 & -7\\-3 & 1 & 4\\5 & -8 & 2\end{matrix}\right] E = \left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right] " data-equation-content=" A = \left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right] B = \left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right] C = \left[\begin{matrix}7 & -2 & -17\end{matrix}\right] D = \left[\begin{matrix}7 & -4 & -7\\-3 & 1 & 4\\5 & -8 & 2\end{matrix}\right] E = \left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\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}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right]+\left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right]=\left[\begin{matrix}14 & 17 & -14\\-11 & -32 & -19\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D13%20%26%2013%20%26%20-15%5C%5C-17%20%26%20-18%20%26%20-6%5Cend%7Bmatrix%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%204%20%26%201%5C%5C6%20%26%20-14%20%26%20-13%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D14%20%26%2017%20%26%20-14%5C%5C-11%20%26%20-32%20%26%20-19%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right]+\left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right]=\left[\begin{matrix}14 & 17 & -14\\-11 & -32 & -19\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}13 & 13 & -15\\-17 & -18 & -6\end{matrix}\right]+\left[\begin{matrix}1 & 4 & 1\\6 & -14 & -13\end{matrix}\right]=\left[\begin{matrix}14 & 17 & -14\\-11 & -32 & -19\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}7 & -2 & -17\end{matrix}\right]\left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right]=\left[\begin{matrix}385 & 307\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D7%20%26%20-2%20%26%20-17%5Cend%7Bmatrix%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Bmatrix%7D3%20%26%200%5C%5C-12%20%26%20-9%5C%5C-20%20%26%20-17%5Cend%7Bmatrix%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D385%20%26%20307%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}7 & -2 & -17\end{matrix}\right]\left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right]=\left[\begin{matrix}385 & 307\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}7 & -2 & -17\end{matrix}\right]\left[\begin{matrix}3 & 0\\-12 & -9\\-20 & -17\end{matrix}\right]=\left[\begin{matrix}385 & 307\end{matrix}\right] " /> </li>
<li> <img class="equation_image" title=" \displaystyle \left[\begin{matrix}34 & 64 & -9\\26 & 49 & -7\\19 & 36 & -5\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D34%20%26%2064%20%26%20-9%5C%5C26%20%26%2049%20%26%20-7%5C%5C19%20%26%2036%20%26%20-5%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}34 & 64 & -9\\26 & 49 & -7\\19 & 36 & -5\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}34 & 64 & -9\\26 & 49 & -7\\19 & 36 & -5\end{matrix}\right] " /> </li>
</ol></p> </p>