Exam 7: Systems and Matrices

Determine the number of solutions to the augmented matrix. $\left[\begin{array}{rrrrr}1 & 2 & 0 & 1 & 4 \\0 & 1 & -1 & -3 & 2 \\0 & 0 & 1 & 3 & 5 \\0 & 0 & 0 & 0 & 1\end{array}\right]$

Solve the system by the substitution method. + =13 y =-1

Find $A^{-1}$ of the matrix $A=\left[\begin{array}{rrr}1 & 0 & 0 \\-3 & 1 & 6 \\5 & 0 & 1\end{array}\right]$

x+2y-3z =19 2x-3y+4z =-17 3x-y =4 equations as a matrix equation AX=B is $\left[\begin{array}{rrr}1 & 2 & -3 \\2 & -3 & 4 \\3 & -1 & 0\end{array}\right]\left[\begin{array}{l}y \\x \\z\end{array}\right]=\left[\begin{array}{r}19 \\-17 \\4\end{array}\right]$ -Use an inverse matrix to solve the system given in above.

Solve the system by the elimination method. 2x-3y=17 4x+5y=1

Solve the linear programming problem. Maximize C=-3x+5y subject to: x-y \geq-3 2x+y \leq12 x \geq0 y \geq0

The inverse of matrix $\left[\begin{array}{rrr}2 & 1 & -1 \\2 & 2 & -1 \\-1 & -1 & 1\end{array}\right] \text { is }\left[\begin{array}{rrr}1 & 0 & 1 \\-1 & 1 & 0 \\0 & 1 & 2\end{array}\right]$ Solve the following system by the method of inverse matrix. 2x+y-z=2 2x+2y-z=4 -x-y+z=-1

Solve the system by elimination. x-y =-2 x+2y =7

Use Gaussian elimination to solve the system. 5x-2y-4z=24 4x-y-5z=18 x+3y-11z=-2

What is the partial fraction decomposition of $\frac{5 x}{x^{2}+x-6} ?$

Solve the system by substitution. x-y =3 y =-5

Use Gaussian elimination to solve the system. 2x+3y-12z=1 x-2y+z=4 4x+y-14z=7

Find the inverse of the matrix $\left[\begin{array}{rr}6 & -8 \\2 & 3\end{array}\right]$

Write the partial fraction decomposition of $\frac{3 x^{2}+4}{\left(x^{2}+1\right)^{2}}$

Solve the system of inequalities graphically. + =36 100+18 \geq1600

Use Gaussian elimination to solve the system. x+2y-3z=-7 2x-3y+z=14 4x+y-2z=3

The system below has an infinite number of solutions. Find the solution set. x+y-5z=3 x-2z=1 2x-y-z=1

Solve the system graphically. Round answers to the nearest hundredth. y=-1+3+2 y=1+4x

Solve the system of inequalities graphically. +\leq25 xy\leq2

Find the determinant of the matrix $A=\left[\begin{array}{rr}1 & 5 \\6 & 10\end{array}\right]$