Study Guide for Exam $2($numbered blue problems are extra practice with answer key at the end$)$

Textbook problems

Topic covered

CD$,$ AAD AED

Section $4\mathrm{.}5$

p$.23579,80$

Use the Cryptography code $($p$\mathrm{.}232)$ to decode an encoded message. Code will be provided on the exam

The following message was encoded using the matrix $A=\left[\begin{array}{cc}2& 3\\ 3& 4\end{array}\right]$

$\backslash$table$[[64,92,10,15,11,16,69,98,33,44,55,78,38,53,40,60]]$

Use the cryptography code on page $232$ of the text to decode this message and reveal the name of a favorite movie of one of your classmates.

Section $4\mathrm{.}6$

p$.24213-16$ Write a given system of equations as a matrix equation of the form $A*x=B$

$2.$ Convert the given system of equations to a matrix equation.

$11x_1-3x_2+9x_3=13$

$-x_1+x_2+,=12$

$x_1+4x_2+x_3=14$

p$.241-42$

$9-12$

Write a given matrix equation as a system of equations without matrices.

$3.$ Convert the given matrix equation to the system of equations it represents.

$\left[\begin{array}{ccc}1& -2& 3\\ 0& -1& 7\\ 1& 3& 2\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}13\\ 2\\ 1\end{array}\right]$

p$.242$

$31-37$ odd

Use matrix inverse methods to solve a given system of equations

$4.$ Use matrix inverse methods to solve the system of equations below for the given values of $k.$ For part A only, show the matrix equation and the equation you used to solve the problem.

$3x_1-x_2+x_3=k_1$

$-x_1+x_2+5x_3=k_2$

$x_1-2x_2+x_3=k_3$

A$)$

$k_1=5$

$k_2=-7$

$k_3=1$

B$)k_1=0$

$k_2=54$

$k_3=5$

C$)$

$k_1=37$

$k_2=7$

$k_3=20$

$($continued on next page$)$