Question 1

Write the augmented matrix for the system.
-

Accepted Answer

A)  $\left[ \begin{array} { r r r } 13 & - 2 & 3 \ 20 & 8 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 3 & - 2 & 20 \ 2 & 8 & 13 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 3 & - 2 & 13 \ 8 & 2 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 3 & 8 & 13 \ - 2 & 2 & 20 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 13 & - 2 & 3 \ 20 & 8 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 3 & - 2 & 20 \ 2 & 8 & 13 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 3 & - 2 & 13 \ 8 & 2 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 3 & 8 & 13 \ - 2 & 2 & 20 \end{array} \right]$

Question 2

Write the augmented matrix for the system.
-

Accepted Answer

A)  $\left[ \begin{array} { r r r r } 8 & - 9 & 0 & 9 \ 4 & - 2 & 0 & - 5 \ - 4 & 0 & 0 & - 4 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 8 & - 9 & 9 & 0 \ 4 & - 2 & - 5 & 0 \ - 6 & - 4 & 0 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r r } 8 & - 9 & 9 & 0 \ 4 & - 2 & 0 & - 5 \ - 6 & 0 & 0 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 8 & - 9 & 0 & 9 \ 0 & 4 & - 2 & - 5 \ 0 & 0 & - 6 & - 4 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r r } 8 & - 9 & 0 & 9 \ 4 & - 2 & 0 & - 5 \ - 4 & 0 & 0 & - 4 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 8 & - 9 & 9 & 0 \ 4 & - 2 & - 5 & 0 \ - 6 & - 4 & 0 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r r } 8 & - 9 & 9 & 0 \ 4 & - 2 & 0 & - 5 \ - 6 & 0 & 0 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 8 & - 9 & 0 & 9 \ 0 & 4 & - 2 & - 5 \ 0 & 0 & - 6 & - 4 \end{array} \right]$

Question 3

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 1134 tickets. Also, they have sold 80 more adult tickets than children's tickets. How
Many adult tickets have they sold?

Accepted Answer

A)  592 
B)  607 
C)  605 
D)  612 
A)  592 
B)  607 
C)  605 
D)  612

Question 4

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { l l } 
9 & 4 \
4 & 4
\end{array} \right] , \left[ \begin{array} { r r } 
- 0.2 & 0.2 \
0.2 & - 0.45
\end{array} \right]$$

Accepted Answer

A) True 
 B)False

Question 5

Use a graph to determine the number of solutions the system has.
-2x - 2y = -4 3x + 3y = -12

Accepted Answer

A)  One solution 
B)  No solution 
C)  Infinitely many solutions 
A)  One solution 
B)  No solution 
C)  Infinitely many solutions

Question 6

Write the augmented matrix for the system.
-

Accepted Answer

A)  $\left[ \begin{array} { r r r } 3 & 0 & 6 \ 0 & 8 & 8 \ 2 & 6 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 3 & 0 & 6 & 0 \ 0 & 8 & 8 & 32 \ 2 & 6 & - 2 & 12 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r r } 3 & 0 & 2 & 0 \ 0 & 8 & 6 & 32 \ 6 & 8 & - 2 & 12 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 3 & 6 & 0 & 0 \ 8 & 8 & 0 & 32 \ 2 & 6 & - 2 & 12 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 3 & 0 & 6 \ 0 & 8 & 8 \ 2 & 6 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 3 & 0 & 6 & 0 \ 0 & 8 & 8 & 32 \ 2 & 6 & - 2 & 12 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r r } 3 & 0 & 2 & 0 \ 0 & 8 & 6 & 32 \ 6 & 8 & - 2 & 12 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 3 & 6 & 0 & 0 \ 8 & 8 & 0 & 32 \ 2 & 6 & - 2 & 12 \end{array} \right]$

Question 7

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { r r r } 
- 4 & 0 & 0 \
0 & - 1 & 0 \
0 & 0 & 2
\end{array} \right]$$

Accepted Answer

A)  Inverse does not exist 
B) 
$$\left[ \begin{array} { c c c } 
\frac { 1 } { - 4 } & 0 & 0 \
0 & - 1 & 0 \
0 & 0 & \frac { 1 } { 2 }
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { c c c } 
0 & 0 & \frac { 1 } { - 4 } \
0 & - 1 & 0 \
\frac { 1 } { 2 } & 0 & 0
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
4 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & - 2
\end{array} \right]$$ 
A)  Inverse does not exist 
B) 
$$\left[ \begin{array} { c c c } 
\frac { 1 } { - 4 } & 0 & 0 \
0 & - 1 & 0 \
0 & 0 & \frac { 1 } { 2 }
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { c c c } 
0 & 0 & \frac { 1 } { - 4 } \
0 & - 1 & 0 \
\frac { 1 } { 2 } & 0 & 0
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
4 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & - 2
\end{array} \right]$$

Question 8

Use Gaussian elimination to solve the system of equations.
-$$\begin{array} { l } 
- 2 x - 7 y = - 6 \
- 4 x = - 8 + 14 y
\end{array}$$

Accepted Answer

A)  $( - 4,2 )$ 
B)  $( 15,22 )$ 
C)  No solution 
D)  $( - 4,22 )$ 
A)  $( - 4,2 )$ 
B)  $( 15,22 )$ 
C)  No solution 
D)  $( - 4,22 )$

Question 9

Solve the system of equations.
-x + y + z - w = 6 2x - y + 3z + 4w = -4
4x + 2y - z - w = -13
-x - 2y + 4z + 3w = 12

Accepted Answer

A)  No solution 
B)  - 14 , 13 , 15 , - 12 
C)  (4, -3, -5, 2) 
D)  (-4, 3, 5, -2) 
A)  No solution 
B)  - 14 , 13 , 15 , - 12 
C)  (4, -3, -5, 2) 
D)  (-4, 3, 5, -2)

Question 10

Solve the system of inequalities.
-$\begin{array}{r}
2 x+3 y \geq 6 \
x-y \geq 3 \
x \geq 1
\end{array}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

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

Accepted Answer

A)  $x \geq - 2$
$y \leq - x ^ { 2 } + 4$ 
B)  $y \leq 2$
$y \geq x ^ { 2 } + 4$ 
C)  $\mathrm { y } \leq - 2$
$y \geq - x ^ { 2 } + 4$ 
D)  $\mathrm { y } \geq - 2$
$y \leq - x ^ { 2 } + 4$ 
A)  $x \geq - 2$
$y \leq - x ^ { 2 } + 4$ 
B)  $y \leq 2$
$y \geq x ^ { 2 } + 4$ 
C)  $\mathrm { y } \leq - 2$
$y \geq - x ^ { 2 } + 4$ 
D)  $\mathrm { y } \geq - 2$
$y \leq - x ^ { 2 } + 4$

Question 12

Find the matrix product, if possible.
-$$\left[ \begin{array} { r r r } 
- 5 & 2 & - 1 \
9 & 7 & - 9
\end{array} \right] \left[ \begin{array} { r r r } 
6 & 8 & - 1 \
6 & - 3 & - 5 \
7 & - 9 & - 1
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r r } 
- 5 & 2 & - 1 \
9 & 7 & - 9 \
6 & 8 & - 1 \
6 & - 3 & - 5 \
7 & - 9 & - 1
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rr}
-25 & 33 \
-37 & 132 \
-4 & -35
\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr}
-30 & 16 & 1 \
54 & -21 & 45 \
63 & -63 & 9
\end{array}\right]$ 
D) 
$\left[\begin{array}{rrr}
-25 & -37 & -4 \
33 & 132 & -35
\end{array}\right]$ 
A) 
$$\left[ \begin{array} { r r r } 
- 5 & 2 & - 1 \
9 & 7 & - 9 \
6 & 8 & - 1 \
6 & - 3 & - 5 \
7 & - 9 & - 1
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rr}
-25 & 33 \
-37 & 132 \
-4 & -35
\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr}
-30 & 16 & 1 \
54 & -21 & 45 \
63 & -63 & 9
\end{array}\right]$ 
D) 
$\left[\begin{array}{rrr}
-25 & -37 & -4 \
33 & 132 & -35
\end{array}\right]$

Question 13

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

Accepted Answer

A)  $- 214$ 
B)  214 
C)  $- 104$ 
D)  $- 94$ 
A)  $- 214$ 
B)  214 
C)  $- 104$ 
D)  $- 94$

Question 14

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { r r r } 
- 2 & 0 & 2 \
2 & 4 & 6 \
- 3 & - 1 & 1
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { c c c } 
- \frac { 1 } { 2 } & 0 & 1 \
0 & \frac { 1 } { 4 } & 0 \
1 & 0 & 1
\end{array} \right]$$ 
B)

$$\left[ \begin{array} { c c c } 
- \frac { 1 } { 2 } & 0 & 0 \
0 & \frac { 1 } { 4 } & 0 \
0 & 0 & 1
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
- \frac { 1 } { 2 } & 0 & \frac { 1 } { 2 } \
\frac { 1 } { 2 } & \frac { 1 } { 4 } & \frac { 1 } { 6 } \
- \frac { 1 } { 3 } & - 1 & 1
\end{array} \right]$$ 
D)  $\text { Inverse does not exist }$ 
A) 
$$\left[ \begin{array} { c c c } 
- \frac { 1 } { 2 } & 0 & 1 \
0 & \frac { 1 } { 4 } & 0 \
1 & 0 & 1
\end{array} \right]$$ 
B)

$$\left[ \begin{array} { c c c } 
- \frac { 1 } { 2 } & 0 & 0 \
0 & \frac { 1 } { 4 } & 0 \
0 & 0 & 1
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
- \frac { 1 } { 2 } & 0 & \frac { 1 } { 2 } \
\frac { 1 } { 2 } & \frac { 1 } { 4 } & \frac { 1 } { 6 } \
- \frac { 1 } { 3 } & - 1 & 1
\end{array} \right]$$ 
D)  $\text { Inverse does not exist }$

Question 15

Solve the problem.
-The sum of a student's three scores is 230. If the first is 25 points more than the second, and the sum of the first two is 5 more than twice the third, what was the first score?

Accepted Answer

A)  90 
B)  75 
C)  50 
D)  65 
A)  90 
B)  75 
C)  50 
D)  65

Question 16

Write the augmented matrix for the system.
-

Accepted Answer

A) 
$\left[ \begin{array} { l l l l } 3 & 4 & 7 & 64 \ 8 & 4 & 2 & 64 \ 2 & 4 & 4 & 40 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } 3 & 8 & 2 & 64 \ 4 & 4 & 4 & 64 \ 7 & 2 & 4 & 40 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 3 & 4 & 7 \ 8 & 4 & 2 \ 2 & 4 & 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } 64 & 7 & 4 & 3 \ 64 & 2 & 4 & 8 \ 40 & 4 & 4 & 2 \end{array} \right]$ 
A) 
$\left[ \begin{array} { l l l l } 3 & 4 & 7 & 64 \ 8 & 4 & 2 & 64 \ 2 & 4 & 4 & 40 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } 3 & 8 & 2 & 64 \ 4 & 4 & 4 & 64 \ 7 & 2 & 4 & 40 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 3 & 4 & 7 \ 8 & 4 & 2 \ 2 & 4 & 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } 64 & 7 & 4 & 3 \ 64 & 2 & 4 & 8 \ 40 & 4 & 4 & 2 \end{array} \right]$

Question 17

Determine the value of each variable.
-$$\left[ \begin{array} { r r } 
5 & - 1 \
9 & 3
\end{array} \right] = \left[ \begin{array} { r r } 
x & - 1 \
y & z
\end{array} \right]$$

Accepted Answer

A)  $x = - 5 ; y = 3 ; z = 9$ 
B)  $x = 9 ; y = 3 ; z = 5$ 
C)  $x = - 5 ; y = - 9 ; z = - 3$ 
D)  $x = 5 ; y = 9 ; z = 3$ 
A)  $x = - 5 ; y = 3 ; z = 9$ 
B)  $x = 9 ; y = 3 ; z = 5$ 
C)  $x = - 5 ; y = - 9 ; z = - 3$ 
D)  $x = 5 ; y = 9 ; z = 3$

Question 18

Find the indicated matrix product or state that the product is undefined.
-$$A = \left[ \begin{array} { l l l } 
0 & 1 & 0 \
0 & 0 & 1 \
1 & 0 & 0
\end{array} \right] , B = \left[ \begin{array} { r r r } 
- 5 & - 4 & - 7 \
- 8 & 9 & - 5 \
- 6 & - 1 & 5
\end{array} \right]$$
BA

Accepted Answer

A)  $\left[\begin{array}{rrr}
-5 & -4 & -7 \
-8 & 9 & -5 \
-6 & -1 & 5
\end{array}\right]$ 
B) $\left[\begin{array}{rrr}
-8 & 9 & -5 \
-6 & -1 & 5 \
-5 & -4 & -7
\end{array}\right]$ 
C)  $\left[\begin{array}{rrr}
0 & -4 & 0 \
0 & 0 & -5 \
-6 & 0 & 0
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-7 & -5 & -4 \
-5 & -8 & 9 \
5 & -6 & -1
\end{array}\right]$ 
A)  $\left[\begin{array}{rrr}
-5 & -4 & -7 \
-8 & 9 & -5 \
-6 & -1 & 5
\end{array}\right]$ 
B) $\left[\begin{array}{rrr}
-8 & 9 & -5 \
-6 & -1 & 5 \
-5 & -4 & -7
\end{array}\right]$ 
C)  $\left[\begin{array}{rrr}
0 & -4 & 0 \
0 & 0 & -5 \
-6 & 0 & 0
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-7 & -5 & -4 \
-5 & -8 & 9 \
5 & -6 & -1
\end{array}\right]$

Question 19

Solve the system of equations.
--x + y + 3z = -1 3x - y + z = -21

Accepted Answer

A)  (3z + 1, z + 21, z) 
B)  (-2z - 10, -5z - 11, z) 
C)  No solution 
D)  (-2z - 11, -5z - 12, z) 
A)  (3z + 1, z + 21, z) 
B)  (-2z - 10, -5z - 11, z) 
C)  No solution 
D)  (-2z - 11, -5z - 12, z)

Question 20

Solve the system of equations by using an inverse matrix.
-$$\begin{array} { c } 
x + 3 y = - 8 \
- 14 x - 4 y = - 2
\end{array}$$

Accepted Answer

A)  $( - 1,3 )$ 
B)  $( - 3,1 )$ 
C)  $( 1 , - 3 )$ 
D)  $( 3 , - 1 )$ 
A)  $( - 1,3 )$ 
B)  $( - 3,1 )$ 
C)  $( 1 , - 3 )$ 
D)  $( 3 , - 1 )$

Write the augmented matrix for the system. -

Write the augmented matrix for the system. -

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 1134 tickets. Also, they have sold 80 more adult tickets than children's tickets. How Many adult tickets have they sold?

Determine whether the matrices are inverses. - $\left[ \begin{array} { l l } 9 & 4 \\4 & 4\end{array} \right] , \left[ \begin{array} { r r } - 0.2 & 0.2 \\0.2 & - 0.45\end{array} \right]$

Use a graph to determine the number of solutions the system has. -2x - 2y = -4 3x + 3y = -12

Write the augmented matrix for the system. -

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { r r r } - 4 & 0 & 0 \\0 & - 1 & 0 \\0 & 0 & 2\end{array} \right]$

Use Gaussian elimination to solve the system of equations. - -2x-7y=-6 -4x=-8+14y

Solve the system of equations. -x + y + z - w = 6 2x - y + 3z + 4w = -4 4x + 2y - z - w = -13 -x - 2y + 4z + 3w = 12

Solve the system of inequalities. - 2x+3y\geq6 x-y\geq3 x\geq1 $Solve the system of inequalities. - \begin{array}{r} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ x \geq 1 \end{array}$

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

Find the matrix product, if possible. - $\left[ \begin{array} { r r r } - 5 & 2 & - 1 \\9 & 7 & - 9\end{array} \right] \left[ \begin{array} { r r r } 6 & 8 & - 1 \\6 & - 3 & - 5 \\7 & - 9 & - 1\end{array} \right]$

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

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { r r r } - 2 & 0 & 2 \\2 & 4 & 6 \\- 3 & - 1 & 1\end{array} \right]$

Solve the problem. -The sum of a student's three scores is 230. If the first is 25 points more than the second, and the sum of the first two is 5 more than twice the third, what was the first score?

Write the augmented matrix for the system. -

Determine the value of each variable. - $\left[ \begin{array} { r r } 5 & - 1 \\9 & 3\end{array} \right] = \left[ \begin{array} { r r } x & - 1 \\y & z\end{array} \right]$

Find the indicated matrix product or state that the product is undefined. - $A = \left[ \begin{array} { l l l } 0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{array} \right] , B = \left[ \begin{array} { r r r } - 5 & - 4 & - 7 \\- 8 & 9 & - 5 \\- 6 & - 1 & 5\end{array} \right]$ BA

Solve the system of equations. --x + y + 3z = -1 3x - y + z = -21

Solve the system of equations by using an inverse matrix. - x+3y=-8 -14x-4y=-2

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 7: Systems and Matrices

Write the augmented matrix for the system. -

Write the augmented matrix for the system. -

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 1134 tickets. Also, they have sold 80 more adult tickets than children's tickets. How Many adult tickets have they sold?

Determine whether the matrices are inverses. - [9444],[−0.20.20.2−0.45]\left[ \begin{array} { l l } 9 & 4 \\4 & 4\end{array} \right] , \left[ \begin{array} { r r } - 0.2 & 0.2 \\0.2 & - 0.45\end{array} \right][94​44​],[−0.20.2​0.2−0.45​]

Use a graph to determine the number of solutions the system has. -2x - 2y = -4 3x + 3y = -12

Write the augmented matrix for the system. -

Find the inverse of A if it has one, or state that the inverse does not exist. - A=[−4000−10002]A = \left[ \begin{array} { r r r } - 4 & 0 & 0 \\0 & - 1 & 0 \\0 & 0 & 2\end{array} \right]A=​−400​0−10​002​​

Use Gaussian elimination to solve the system of equations. - -2x-7y=-6 -4x=-8+14y

Solve the system of equations. -x + y + z - w = 6 2x - y + 3z + 4w = -4 4x + 2y - z - w = -13 -x - 2y + 4z + 3w = 12

Solve the system of inequalities. - 2x+3y\geq6 x-y\geq3 x\geq1

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

Find the determinant of the given matrix. - [−1−35−5−1−5−441]\left[ \begin{array} { r r r } - 1 & - 3 & 5 \\- 5 & - 1 & - 5 \\- 4 & 4 & 1\end{array} \right]​−1−5−4​−3−14​5−51​​

Find the inverse of A if it has one, or state that the inverse does not exist. - A=[−202246−3−11]A = \left[ \begin{array} { r r r } - 2 & 0 & 2 \\2 & 4 & 6 \\- 3 & - 1 & 1\end{array} \right]A=​−22−3​04−1​261​​

Solve the problem. -The sum of a student's three scores is 230. If the first is 25 points more than the second, and the sum of the first two is 5 more than twice the third, what was the first score?

Write the augmented matrix for the system. -

Determine the value of each variable. - [5−193]=[x−1yz]\left[ \begin{array} { r r } 5 & - 1 \\9 & 3\end{array} \right] = \left[ \begin{array} { r r } x & - 1 \\y & z\end{array} \right][59​−13​]=[xy​−1z​]

Solve the system of equations. --x + y + 3z = -1 3x - y + z = -21

Solve the system of equations by using an inverse matrix. - x+3y=-8 -14x-4y=-2

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Determine whether the matrices are inverses. - $\left[ \begin{array} { l l } 9 & 4 \\4 & 4\end{array} \right] , \left[ \begin{array} { r r } - 0.2 & 0.2 \\0.2 & - 0.45\end{array} \right]$

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { r r r } - 4 & 0 & 0 \\0 & - 1 & 0 \\0 & 0 & 2\end{array} \right]$

Solve the system of inequalities. - 2x+3y\geq6 x-y\geq3 x\geq1 $Solve the system of inequalities. - \begin{array}{r} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ x \geq 1 \end{array}$

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

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { r r r } - 2 & 0 & 2 \\2 & 4 & 6 \\- 3 & - 1 & 1\end{array} \right]$

Determine the value of each variable. - $\left[ \begin{array} { r r } 5 & - 1 \\9 & 3\end{array} \right] = \left[ \begin{array} { r r } x & - 1 \\y & z\end{array} \right]$