Question 1

Solve the system by elimination.
-$$\begin{array} { c } 
x + 3 y = - 15 \
- 3 x + 4 y = - 20
\end{array}$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ ( 1 , - 6 ) \}$ 
C)  $\{ ( 5,0 ) \}$ 
D)  $\{ ( 0 , - 5 ) \}$ 
A)  $\varnothing$ 
B)  $\{ ( 1 , - 6 ) \}$ 
C)  $\{ ( 5,0 ) \}$ 
D)  $\{ ( 0 , - 5 ) \}$ D

Question 2

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { c } 
x ^ { 2 } - x y + y ^ { 2 } = 3 \
2 x ^ { 2 } + x y + 2 y ^ { 2 } = 12
\end{array}$$

Accepted Answer

A)  $\{ ( 1,0 ) , ( - 1,0 ) \}$ 
B)  $\{ ( 2,1 ) , ( 1,2 ) \}$ 
C)  $\{ ( 2,0 ) , ( - 2,0 ) , ( 1,0 ) , ( - 1,0 ) \}$ 
D)  $\{ ( 2,1 ) , ( - 2 , - 1 ) , ( 1,2 ) , ( - 1 , - 2 ) \}$ 
A)  $\{ ( 1,0 ) , ( - 1,0 ) \}$ 
B)  $\{ ( 2,1 ) , ( 1,2 ) \}$ 
C)  $\{ ( 2,0 ) , ( - 2,0 ) , ( 1,0 ) , ( - 1,0 ) \}$ 
D)  $\{ ( 2,1 ) , ( - 2 , - 1 ) , ( 1,2 ) , ( - 1 , - 2 ) \}$ D

Question 3

Find the partial fraction decomposition for the rational expression.
-$$\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }$$

Accepted Answer

A)  $\frac { 4 } { 3 x + 4 } + \frac { 2 } { ( x + 1 ) ^ { 2 } } + \frac { - 3 } { x + 1 }$ 
B)  $\frac { 4 } { 3 x + 4 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } } + \frac { - 2 } { x + 1 }$ 
C)  $\frac { 4 } { 3 x + 4 } + \frac { 3 } { ( x + 1 ) ^ { 2 } } + \frac { 2 } { x + 1 }$ 
D)  $\frac { 4 } { 3 x + 4 } + \frac { - 2 } { x + 1 } + \frac { 3 } { ( x + 1 ) ^ { 2 } }$ 
A)  $\frac { 4 } { 3 x + 4 } + \frac { 2 } { ( x + 1 ) ^ { 2 } } + \frac { - 3 } { x + 1 }$ 
B)  $\frac { 4 } { 3 x + 4 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } } + \frac { - 2 } { x + 1 }$ 
C)  $\frac { 4 } { 3 x + 4 } + \frac { 3 } { ( x + 1 ) ^ { 2 } } + \frac { 2 } { x + 1 }$ 
D)  $\frac { 4 } { 3 x + 4 } + \frac { - 2 } { x + 1 } + \frac { 3 } { ( x + 1 ) ^ { 2 } }$ D

Question 4

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge
of the concepts involved in graphing inequalities.
-

Accepted Answer

A)  $y \leq x$ 
B)  $y \geq x$ 
C)  $y \leq - x$ 
D)  $y \geq - x$ 
A)  $y \leq x$ 
B)  $y \geq x$ 
C)  $y \leq - x$ 
D)  $y \geq - x$

Question 5

Solve the problem.
-The sum of the squares of the digits of a positive two-digit number is 13 , and the units digit is 1 more than the tens digit. Find the number.

Accepted Answer

A)  32 
B)  43 
C)  34 
D)  23 
A)  32 
B)  43 
C)  34 
D)  23

Question 6

Find the indicated matrix.
-Let $A = \left[ \begin{array} { l l } 3 & 3 \ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \ - 1 & 6 \end{array} \right]$. Find $3 A + B$.

Accepted Answer

A) 
$\left[ \begin{array} { l l } 9 & 13 \ 1 & 11 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l l } 9 & 21 \ 3 & 33 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 9 & 7 \ 5 & 11 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l l } 9 & 13 \ 5 & 21 \end{array} \right]$ 
A) 
$\left[ \begin{array} { l l } 9 & 13 \ 1 & 11 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l l } 9 & 21 \ 3 & 33 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 9 & 7 \ 5 & 11 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l l } 9 & 13 \ 5 & 21 \end{array} \right]$

Question 7

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { r } 
- 2 x - 6 y - z = - 18 \
x - 7 y + 8 z = 59 \
- 4 x + y + z = 1
\end{array}$$

Accepted Answer

A)  $\{ ( 2 , - 1 , - 8 ) \}$ 
B)  $\{ ( 1,8,1 ) \}$ 
C)  $\{ ( 2,1,8 ) \}$ 
D)  $\{ ( 3 , - 1,8 ) \}$ 
A)  $\{ ( 2 , - 1 , - 8 ) \}$ 
B)  $\{ ( 1,8,1 ) \}$ 
C)  $\{ ( 2,1,8 ) \}$ 
D)  $\{ ( 3 , - 1,8 ) \}$

Question 8

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form.
-

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } \leq 16$
$y \geq 0$ 
B)  $x ^ { 2 } + y ^ { 2 } \geq 16$
$x \geq 0$ 
C)  $x ^ { 2 } + y ^ { 2 } \leq 16$
$x \leq 0$ 
D)  $x ^ { 2 } + y ^ { 2 } \leq 16$
$x \geq 0$ 
A)  $x ^ { 2 } + y ^ { 2 } \leq 16$
$y \geq 0$ 
B)  $x ^ { 2 } + y ^ { 2 } \geq 16$
$x \geq 0$ 
C)  $x ^ { 2 } + y ^ { 2 } \leq 16$
$x \leq 0$ 
D)  $x ^ { 2 } + y ^ { 2 } \leq 16$
$x \geq 0$

Question 9

Find the partial fraction decomposition for the rational expression.
-$$\frac { 3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 13 } { ( x + 2 ) ( x - 1 ) ^ { 4 } }$$

Accepted Answer

A)  $\frac { 3 } { x + 2 } + \frac { 1 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } } + \frac { 2 } { ( x - 1 ) ^ { 3 } } + \frac { 1 } { ( x - 1 ) ^ { 4 } }$ 
B)  $\frac { - 1 } { x + 2 } + \frac { 5 } { x - 1 } + \frac { 2 } { ( x - 1 ) ^ { 2 } } + \frac { 17 } { ( x - 1 ) ^ { 3 } } + \frac { 12 } { ( x - 1 ) ^ { 4 } }$ 
C)  $\frac { 5 } { x + 2 } + \frac { 7 } { x - 1 } + \frac { - 2 } { ( x - 1 ) ^ { 2 } } + \frac { 4 } { ( x - 1 ) ^ { 3 } } + \frac { 3 } { ( x - 1 ) ^ { 4 } }$ 
D)  $\frac { 1 } { x + 2 } + \frac { 2 } { x - 1 } + \frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 5 } { ( x - 1 ) ^ { 3 } } + \frac { 10 } { ( x - 1 ) ^ { 4 } }$ 
A)  $\frac { 3 } { x + 2 } + \frac { 1 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } } + \frac { 2 } { ( x - 1 ) ^ { 3 } } + \frac { 1 } { ( x - 1 ) ^ { 4 } }$ 
B)  $\frac { - 1 } { x + 2 } + \frac { 5 } { x - 1 } + \frac { 2 } { ( x - 1 ) ^ { 2 } } + \frac { 17 } { ( x - 1 ) ^ { 3 } } + \frac { 12 } { ( x - 1 ) ^ { 4 } }$ 
C)  $\frac { 5 } { x + 2 } + \frac { 7 } { x - 1 } + \frac { - 2 } { ( x - 1 ) ^ { 2 } } + \frac { 4 } { ( x - 1 ) ^ { 3 } } + \frac { 3 } { ( x - 1 ) ^ { 4 } }$ 
D)  $\frac { 1 } { x + 2 } + \frac { 2 } { x - 1 } + \frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 5 } { ( x - 1 ) ^ { 3 } } + \frac { 10 } { ( x - 1 ) ^ { 4 } }$

Question 10

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 36 \
x ^ { 2 } - y ^ { 2 } = 36
\end{array}$$

Accepted Answer

A)  $\{ ( 6,0 ) \}$ 
B)  $\{ ( 0 , - 6 ) \}$ 
C)  $\{ ( 6,0 ) , ( - 6,0 ) \}$ 
D)  $\{ ( 0,6 ) , ( 0 , - 6 ) \}$ 
A)  $\{ ( 6,0 ) \}$ 
B)  $\{ ( 0 , - 6 ) \}$ 
C)  $\{ ( 6,0 ) , ( - 6,0 ) \}$ 
D)  $\{ ( 0,6 ) , ( 0 , - 6 ) \}$

Question 11

Which of the following properties do not hold for matrix multiplication? (i) Associative property
(ii) Commutative property
(iii) Distributive property
(iv) Zero-factor property (If the product of two matrices is a zero matrix, then one of the factors must be a zero matrix.)

Accepted Answer

A)  (ii) 
B)  (i), (iii) 
C)  (ii), (iv) 
D)  None. All of the properties hold. 
A)  (ii) 
B)  (i), (iii) 
C)  (ii), (iv) 
D)  None. All of the properties hold.

Question 12

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
-$$a x + y = \frac { 1 } { a }$$
$$b x + y = \frac { 1 } { b }$$

Accepted Answer

A)  $\left\{ \left( \frac { 1 } { a b } , \frac { a - b } { a b } \right) \right\}$ 
B)  $\left\{ \left( \frac { 1 } { a b } , a + b \right) \right\}$ 
C)  $\left\{ \left( - \frac { 1 } { a b } , \frac { a + b } { a b } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 1 } { a b } , \frac { b - a } { a b } \right) \right\}$ 
A)  $\left\{ \left( \frac { 1 } { a b } , \frac { a - b } { a b } \right) \right\}$ 
B)  $\left\{ \left( \frac { 1 } { a b } , a + b \right) \right\}$ 
C)  $\left\{ \left( - \frac { 1 } { a b } , \frac { a + b } { a b } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 1 } { a b } , \frac { b - a } { a b } \right) \right\}$

Question 13

Provide an appropriate response.
-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?

Accepted Answer

The answer of Provide an appropriate response.
-When using the substitution...

Question 14

Decide whether or not the matrices are inverses of each other.
-$\left[ \begin{array} { r r } 6 & - 5 \ - 3 & 5 \end{array} \right]$ and $\left[ \begin{array} { l l } \frac { 1 } { 3 } & \frac { 1 } { 3 } \ \frac { 1 } { 5 } & \frac { 2 } { 5 } \end{array} \right]$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 15

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge
of the concepts involved in graphing inequalities.
-

Accepted Answer

A)  $y \geq - 2 x - 2$ 
B)  $y \geq 2 x - 2$ 
C)  $y \leq - 2 x - 2$ 
D)  $y \leq 2 x - 2$ 
A)  $y \geq - 2 x - 2$ 
B)  $y \geq 2 x - 2$ 
C)  $y \leq - 2 x - 2$ 
D)  $y \leq 2 x - 2$

Question 16

Solve the linear programming problem.
-Zach is planning to invest up to $\$ 40,000$ in corporate and municipal bonds. The least he will invest in corporate bonds is $\$ 8000$ and he does not want to invest more than $\$ 25,000$ in corporate bonds. He also does not want to invest more than $\$ 33,621$ in municipal bonds. The interest is $8.6 \%$ on corporate bonds and $6.3 \%$ on municipal bonds. This is simple interest for one year. What is the maximum income?

Accepted Answer

A)  $\$ 28,095$ 
B)  $\$ 18,095$ 
C)  $\$ 3095$ 
D)  $\$ 11,205$ 
A)  $\$ 28,095$ 
B)  $\$ 18,095$ 
C)  $\$ 3095$ 
D)  $\$ 11,205$

Question 17

Evaluate the determinant.
-$\left| \begin{array} { l l l l } 4 & 3 & 8 & 5 \ 9 & 8 & 5 & 9 \ 3 & 0 & 0 & 1 \ 2 & 1 & 9 & 2 \end{array} \right|$

Accepted Answer

A)  47 
B)  $- 29$ 
C)  8 
D)  199 
A)  47 
B)  $- 29$ 
C)  8 
D)  199

Question 18

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
-$$\begin{array} { l } 
3 x + y = 13 \
3 x + 3 y = 9
\end{array}$$

Accepted Answer

A)  $\{ ( - 2,5 ) \}$ 
B)  $\{ ( - 2 , - 5 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 5 , - 2 ) \}$ 
A)  $\{ ( - 2,5 ) \}$ 
B)  $\{ ( - 2 , - 5 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 5 , - 2 ) \}$

Question 19

Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { c c } - 2 & 3 \ 14 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Accepted Answer

A) 
$\left[ \begin{array} { r r } - 14 & 21 \ 14 & 0 \end{array} \right]$ 
B) 
$\left[\begin{array}{rr}
-2 & 3 \
0 & 21
\end{array}\right]$ 
C) 
$\left[\begin{array}{rr}
-2 & -11 \
0 & 21
\end{array}\right]$ 
D) 
$\left[\begin{array}{rr}
-2 & 3 \
14 & 21
\end{array}\right]$ 
A) 
$\left[ \begin{array} { r r } - 14 & 21 \ 14 & 0 \end{array} \right]$ 
B) 
$\left[\begin{array}{rr}
-2 & 3 \
0 & 21
\end{array}\right]$ 
C) 
$\left[\begin{array}{rr}
-2 & -11 \
0 & 21
\end{array}\right]$ 
D) 
$\left[\begin{array}{rr}
-2 & 3 \
14 & 21
\end{array}\right]$

Question 20

Find the value of the determinant.
-$\left| \begin{array} { l l l } 5 & 4 & 3 \ 5 & 4 & 4 \ 1 & 3 & 4 \end{array} \right|$

Accepted Answer

A)  $- 11$ 
B)  11 
C)  293 
D)  $- 43$ 
A)  $- 11$ 
B)  11 
C)  293 
D)  $- 43$

Solve the system by elimination. - x+3y=-15 -3x+4y=-20

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - -xy+=3 2+xy+2=12

Find the partial fraction decomposition for the rational expression. - $\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Solve the problem. -The sum of the squares of the digits of a positive two-digit number is 13 , and the units digit is 1 more than the tens digit. Find the number.

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } 3 & 3 \\ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]$ . Find $3 A + B$ .

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - -2x-6y-z=-18 x-7y+8z=59 -4x+y+z=1

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Find the partial fraction decomposition for the rational expression. - $\frac { 3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 13 } { ( x + 2 ) ( x - 1 ) ^ { 4 } }$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=36 -=36

Which of the following properties do not hold for matrix multiplication? (i) Associative property (ii) Commutative property (iii) Distributive property (iv) Zero-factor property (If the product of two matrices is a zero matrix, then one of the factors must be a zero matrix.)

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - $a x + y = \frac { 1 } { a }$ $b x + y = \frac { 1 } { b }$

Provide an appropriate response. -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?

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r } 6 & - 5 \\ - 3 & 5 \end{array} \right]$ and $\left[ \begin{array} { l l } \frac { 1 } { 3 } & \frac { 1 } { 3 } \\ \frac { 1 } { 5 } & \frac { 2 } { 5 } \end{array} \right]$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Evaluate the determinant. - $\left| \begin{array} { l l l l } 4 & 3 & 8 & 5 \\ 9 & 8 & 5 & 9 \\ 3 & 0 & 0 & 1 \\ 2 & 1 & 9 & 2 \end{array} \right|$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 3x+y=13 3x+3y=9

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { c c } - 2 & 3 \\ 14 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Find the value of the determinant. - $\left| \begin{array} { l l l } 5 & 4 & 3 \\ 5 & 4 & 4 \\ 1 & 3 & 4 \end{array} \right|$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 9: Systems and Matrices

Solve the system by elimination. - x+3y=-15 -3x+4y=-20

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - -xy+=3 2+xy+2=12

Find the partial fraction decomposition for the rational expression. - −2x2+3x+8(x+1)2(3x+4)\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }(x+1)2(3x+4)−2x2+3x+8​

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Solve the problem. -The sum of the squares of the digits of a positive two-digit number is 13 , and the units digit is 1 more than the tens digit. Find the number.

Find the indicated matrix. -Let A=[3325]A = \left[ \begin{array} { l l } 3 & 3 \\ 2 & 5 \end{array} \right]A=[32​35​] and B=[04−16]B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]B=[0−1​46​] . Find 3A+B3 A + B3A+B .

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - -2x-6y-z=-18 x-7y+8z=59 -4x+y+z=1

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Find the partial fraction decomposition for the rational expression. - 3x4−3x3+5x2+12x+13(x+2)(x−1)4\frac { 3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 13 } { ( x + 2 ) ( x - 1 ) ^ { 4 } }(x+2)(x−1)43x4−3x3+5x2+12x+13​

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=36 -=36

Which of the following properties do not hold for matrix multiplication? (i) Associative property (ii) Commutative property (iii) Distributive property (iv) Zero-factor property (If the product of two matrices is a zero matrix, then one of the factors must be a zero matrix.)

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - ax+y=1aa x + y = \frac { 1 } { a }ax+y=a1​ bx+y=1bb x + y = \frac { 1 } { b }bx+y=b1​

Provide an appropriate response. -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?

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Evaluate the determinant. - ∣4385985930012192∣\left| \begin{array} { l l l l } 4 & 3 & 8 & 5 \\ 9 & 8 & 5 & 9 \\ 3 & 0 & 0 & 1 \\ 2 & 1 & 9 & 2 \end{array} \right|​4932​3801​8509​5912​​

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 3x+y=13 3x+3y=9

Use the given row transformation to change the matrix as indicated. - [−23140];7\left[ \begin{array} { c c } - 2 & 3 \\ 14 & 0 \end{array} \right] ; 7[−214​30​];7 times row 1 added to row 2

Find the value of the determinant. - ∣543544134∣\left| \begin{array} { l l l } 5 & 4 & 3 \\ 5 & 4 & 4 \\ 1 & 3 & 4 \end{array} \right|​551​443​344​​

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Find the partial fraction decomposition for the rational expression. - $\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }$

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } 3 & 3 \\ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]$ . Find $3 A + B$ .

Find the partial fraction decomposition for the rational expression. - $\frac { 3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 13 } { ( x + 2 ) ( x - 1 ) ^ { 4 } }$

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - $a x + y = \frac { 1 } { a }$ $b x + y = \frac { 1 } { b }$

Evaluate the determinant. - $\left| \begin{array} { l l l l } 4 & 3 & 8 & 5 \\ 9 & 8 & 5 & 9 \\ 3 & 0 & 0 & 1 \\ 2 & 1 & 9 & 2 \end{array} \right|$

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { c c } - 2 & 3 \\ 14 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Find the value of the determinant. - $\left| \begin{array} { l l l } 5 & 4 & 3 \\ 5 & 4 & 4 \\ 1 & 3 & 4 \end{array} \right|$