Exam 6: Systems of Linear Equations and Matrices

Find the inverse, if it exists, of the given matrix. - $\mathrm{A}=\left[\begin{array}{rr}-5 & 5 \\ 0 & -1\end{array}\right]$

Solve the problem by writing and solving a suitable system of equations. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 159$ for 3 days and 300 miles, while Mary was charged $\$ 289$ for 5 days and 600 miles. What does Best Rental charge per day and per mile?

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $A=\left[\begin{array}{rrr}1 & 3 & -3 \\ 2 & 0 & 3\end{array}\right], B=\left[\begin{array}{rr}3 & 0 \\ -3 & 1 \\ 0 & 3\end{array}\right]$ Find $A B$ .

Write a matrix to display the information. -The matrices give points and rebounds for five starting players in two games. Find the matrix that gives the totals.

Solve the system by using the inverse of the coefficient matrix. - $x-y+2 z=-6$ $4 x+z=-1$ $\mathrm{x}+5 \mathrm{y}+\mathrm{z}=19$

Solve the system by using the inverse of the coefficient matrix. - $x+y+z=-3$ $x-y+3 z=-21$ $4 \mathrm{x}+\mathrm{y}+\mathrm{z}=-9$

Perform the indicated operation where possible. -

Solve the system of equations. If the system is dependent, express solutions in terms of the parameter $\mathrm{z}$ . - $x+4 y+3 z=-6$ $3 y+2 z=-8$ $z=2$

Determine whether the given ordered set of numbers is a solution of the system of equations. -(-6,-2) $\mathrm{x}+\mathrm{y}=-8$ $\mathrm{x}-\mathrm{y}=-4$

Solve the problem by writing and solving a suitable system of equations. -If 40 pounds of tomatoes and 20 pounds of bananas cost $\$ 26$ and 10 pounds of tomatoes and 30 pounds of bananas cost $\$ 14$ , what is the price per pound of tomatoes and bananas

Solve the system of two equations in two variables. - $6 x-98=8 y$ $-3 x+5 y=-56$

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $\mathrm{A}=\left[\begin{array}{rr}3 & -2 \\ 4 & 0\end{array}\right], \mathrm{B}=\left[\begin{array}{rr}0 & -2 \\ 3 & 6\end{array}\right]$ Find $\mathrm{AB}$ .

Find the production matrix for the input-output and demand matrices. - $\mathrm{A}=\left[\begin{array}{cc}\frac{3}{5} & \frac{1}{5} \\ \frac{1}{10} & \frac{7}{10}\end{array}\right], \mathrm{D}=\left[\begin{array}{l}3 \\ 5\end{array}\right]$

given a system of two linear equations in two variables, if the graphs of the two equations coincide, then the system is independent.

Use the Gauss-Jordan method to solve the system of equations. - $3 x+y+z=5$ $4 \mathrm{x}+5 \mathrm{y}-\mathrm{z}=-8$ $10 \mathrm{x}+7 \mathrm{y}+\mathrm{z}=2$

Perform the indicated operation where possible. - $\left[\begin{array}{ll}24\end{array}\right]+\left[\begin{array}{r}-1 \\ 7\end{array}\right]$

Solve the system of two equations in two variables. - $4 x+3 y=2$ $24 x+18 y=12$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x+y+z=-1$ $x-y+3 z=-5$ $3 x+y+z=-3$

Write the word or phrase that best completes each statement or answers the question -Using the matrices $L=\left[\begin{array}{ccc}1 & m & n \\ p & q & r\end{array}\right], X=\left[\begin{array}{lll}x & y & z \\ u & v & w\end{array}\right]$ , and $A=\left[\begin{array}{lll}a & b & c \\ d & e & f\end{array}\right]$ , verify that $\mathrm{L}+(\mathrm{X}+\mathrm{A})=(\mathrm{L}+\mathrm{X})+\mathrm{A}$ .

given a system of two linear equations in two variables, if the graphs of the two equations are distinct parallel lines, then the system has no solution.