\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Evaluate the expression \(\displaystyle 4 A - 5 B + 7 C\)
\begin{equation*} A = \left[\begin{matrix}-3 & 9 & -3\\6 & 7 & -2\\-8 & 5 & -8\\-3 & -8 & -3\end{matrix}\right],\quad\quad B = \left[\begin{matrix}2 & -7 & -5\\2 & 9 & -4\\-2 & -3 & 1\\-5 & -4 & 6\end{matrix}\right], \text{ and } \quad C = \left[\begin{matrix}0 & -6 & -3\\7 & 9 & 9\\-3 & 5 & 6\\8 & 2 & -7\end{matrix}\right]. \end{equation*}
The sum is \(\displaystyle \left[\begin{matrix}-22 & 29 & -8\\63 & 46 & 75\\-43 & 70 & 5\\69 & 2 & -91\end{matrix}\right]\).
\begin{question}Evaluate the expression $4 A - 5 B + 7 C$\newline\begin{equation*} A = \left[\begin{matrix}-3 & 9 & -3\\6 & 7 & -2\\-8 & 5 & -8\\-3 & -8 & -3\end{matrix}\right],\quad\quad B = \left[\begin{matrix}2 & -7 & -5\\2 & 9 & -4\\-2 & -3 & 1\\-5 & -4 & 6\end{matrix}\right], \text{ and } \quad C = \left[\begin{matrix}0 & -6 & -3\\7 & 9 & 9\\-3 & 5 & 6\\8 & 2 & -7\end{matrix}\right]. \end{equation*}
\soln{9cm}{The sum is $\left[\begin{matrix}-22 & 29 & -8\\63 & 46 & 75\\-43 & 70 & 5\\69 & 2 & -91\end{matrix}\right]$. }
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Evaluate the expression <img class="equation_image" title=" \displaystyle 4 A - 5 B + 7 C " src="/equation_images/%20%5Cdisplaystyle%204%20A%20-%205%20B%20%2B%207%20C%20" alt="LaTeX: \displaystyle 4 A - 5 B + 7 C " data-equation-content=" \displaystyle 4 A - 5 B + 7 C " /> <br> <img class="equation_image" title=" A = \left[\begin{matrix}-3 & 9 & -3\\6 & 7 & -2\\-8 & 5 & -8\\-3 & -8 & -3\end{matrix}\right],\quad\quad B = \left[\begin{matrix}2 & -7 & -5\\2 & 9 & -4\\-2 & -3 & 1\\-5 & -4 & 6\end{matrix}\right], \text{ and } \quad C = \left[\begin{matrix}0 & -6 & -3\\7 & 9 & 9\\-3 & 5 & 6\\8 & 2 & -7\end{matrix}\right]. " src="/equation_images/%20%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-3%20%26%209%20%26%20-3%5C%5C6%20%26%207%20%26%20-2%5C%5C-8%20%26%205%20%26%20-8%5C%5C-3%20%26%20-8%20%26%20-3%5Cend%7Bmatrix%7D%5Cright%5D%2C%5Cquad%5Cquad%20B%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D2%20%26%20-7%20%26%20-5%5C%5C2%20%26%209%20%26%20-4%5C%5C-2%20%26%20-3%20%26%201%5C%5C-5%20%26%20-4%20%26%206%5Cend%7Bmatrix%7D%5Cright%5D%2C%20%5Ctext%7B%20and%20%7D%20%5Cquad%20C%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D0%20%26%20-6%20%26%20-3%5C%5C7%20%26%209%20%26%209%5C%5C-3%20%26%205%20%26%206%5C%5C8%20%26%202%20%26%20-7%5Cend%7Bmatrix%7D%5Cright%5D.%20%20" alt="LaTeX: A = \left[\begin{matrix}-3 & 9 & -3\\6 & 7 & -2\\-8 & 5 & -8\\-3 & -8 & -3\end{matrix}\right],\quad\quad B = \left[\begin{matrix}2 & -7 & -5\\2 & 9 & -4\\-2 & -3 & 1\\-5 & -4 & 6\end{matrix}\right], \text{ and } \quad C = \left[\begin{matrix}0 & -6 & -3\\7 & 9 & 9\\-3 & 5 & 6\\8 & 2 & -7\end{matrix}\right]. " data-equation-content=" A = \left[\begin{matrix}-3 & 9 & -3\\6 & 7 & -2\\-8 & 5 & -8\\-3 & -8 & -3\end{matrix}\right],\quad\quad B = \left[\begin{matrix}2 & -7 & -5\\2 & 9 & -4\\-2 & -3 & 1\\-5 & -4 & 6\end{matrix}\right], \text{ and } \quad C = \left[\begin{matrix}0 & -6 & -3\\7 & 9 & 9\\-3 & 5 & 6\\8 & 2 & -7\end{matrix}\right]. " /> </p> </p><p> <p>The sum is <img class="equation_image" title=" \displaystyle \left[\begin{matrix}-22 & 29 & -8\\63 & 46 & 75\\-43 & 70 & 5\\69 & 2 & -91\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D-22%20%26%2029%20%26%20-8%5C%5C63%20%26%2046%20%26%2075%5C%5C-43%20%26%2070%20%26%205%5C%5C69%20%26%202%20%26%20-91%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}-22 & 29 & -8\\63 & 46 & 75\\-43 & 70 & 5\\69 & 2 & -91\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}-22 & 29 & -8\\63 & 46 & 75\\-43 & 70 & 5\\69 & 2 & -91\end{matrix}\right] " /> . </p> </p>