Exam 7: Systems and Matrices

Graph the system of inequalities. Shade the region that represents the solution set. - +y\leq1 -y\leq3

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Solve. -A rectangular plot has area 126 yd2 with a perimeter of 46 yd. What is the length of the longest side?

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - x+4y=6 -3x-y=4 -3x+4y=30

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { r r r } 6 & 0 & 0 \\0 & - 6 & 0 \\6 & 0 & 6\end{array} \right]$

Determine the value of each variable. - $\left[ \begin{array} { l } \mathrm { a } \\ 6 \\ 8 \end{array} \right] = \left[ \begin{array} { l } 8 \\ x \\ 8 \end{array} \right]$

Use the graph to estimate any solutions of the system. - x+3y=-3 2x+6y=-12 $[ - 5,5 ]$ by $[ - 5,5 ]$

Solve the system by substitution. -x + 5y = 11 -2x - 10y = -12

Solve the system by elimination. --4x + 9y = -71 -8x = -73 - 18y

Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of d(x). Then find the partial fraction decomposition of r(x)/d(x). - $\frac { x ^ { 5 } - 3 x ^ { 4 } + x ^ { 3 } - 3 x ^ { 2 } - 6 x - 1 } { x ^ { 2 } - 4 x + 3 }$

Find the matrix product, if possible. - $\left[ \begin{array} { r r r } 1 & 3 & - 1 \\3 & 0 & 5\end{array} \right] \left[ \begin{array} { r r } 3 & 0 \\- 1 & 1 \\0 & 5\end{array} \right]$

Solve the problem. -A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 1120 tickets. Also, they have sold 4 times as many adult tickets as children's tickets. How many adult tickets have they sold?

Use a graph to determine the number of solutions the system has. - 4x+6y=2 10x+15y=5

When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 7. What does this indicate to you about the system of equations?

Perform the indicated operation, if possible. - $\left[ \begin{array} { l l l } - 2 & 8 & 4 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right]$

+=36 -=9 Explain the steps you would use to solve this system by the elimination method.

Find the partial fraction decomposition. - $\frac { 35 x - 98 } { 6 x ^ { 2 } - 35 x + 49 }$

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l } 2 & 3 & 3 \\ 3 & 4 & 4 \\ 5 & 1 & 5 \end{array} \right]$

Write a system of inequalities whose solution set is the region shown. -

Solve the system by substitution. -x - 7y = -56 9x - 7y = -112