Question 1

Graph the inequality.
-$x-y<-2$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 2

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 61 \
x - y = 1
\end{array} \right.$$

Accepted Answer

A)  x = 4, y = 5; x = 5, y = 4 
B)  x = 4, y = -5; x = 5, y = -4 
C)  x = -4, y = -5; x = 5, y = 4 
D)  x = -4, y = 5; x = -5, y = 4 
A)  x = 4, y = 5; x = 5, y = 4 
B)  x = 4, y = -5; x = 5, y = -4 
C)  x = -4, y = -5; x = 5, y = 4 
D)  x = -4, y = 5; x = -5, y = 4

Question 3

Write the augmented matrix for the system.
-$$\left\{ \begin{array} { l } 
9 x + 8 y = 50 \
5 x + 6 y = 34
\end{array} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { l l | l } 2 & 6 & 26 \ 5 & 9 & 35 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l | l } 26 & 6 & 2 \ 35 & 5 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l | l } 2 & 6 \end{array} \right.$ 
D)  $\left[ \begin{array} { l l | l } 2 & 5 & 26 \ 6 & 9 & 35 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l | l } 2 & 6 & 26 \ 5 & 9 & 35 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l | l } 26 & 6 & 2 \ 35 & 5 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l | l } 2 & 6 \end{array} \right.$ 
D)  $\left[ \begin{array} { l l | l } 2 & 5 & 26 \ 6 & 9 & 35 \end{array} \right]$

Question 4

Graph the system of inequalities.
-$$\begin{array} { l } 
y \geq x ^ { 2 } \
x + y > 2 \

\end{array}$$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 5

Use the elimination method to solve the system.
-$$\left\{ \begin{array} { l } 
x + y = - 8 \
x - y = 12
\end{array} \right.$$

Accepted Answer

A)  x = 5, y = 14 
B)  x = 8, y = -10 
C)  x = 2, y = -10 
D)  x = 9, y = 5 
A)  x = 5, y = 14 
B)  x = 8, y = -10 
C)  x = 2, y = -10 
D)  x = 9, y = 5

Question 6

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
9 x - 2 y - z = 64 \
x - 3 y - 3 z = - 27 \
- 6 x + y + z = - 42
\end{array} \right.$$

Accepted Answer

A)  x = 10, y = 3, z = 7 
B)  x = 9, y = -5, z = -7 
C)  x = 5, y = 7, z = 5 
D)  x = 9, y = 5, z = 7 
A)  x = 10, y = 3, z = 7 
B)  x = 9, y = -5, z = -7 
C)  x = 5, y = 7, z = 5 
D)  x = 9, y = 5, z = 7

Question 7

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$$\left[ \begin{array} { r r r r } 
1 & - 9 & 0 & 0 \
0 & 1 & - 7 & 0 \
0 & 0 & 1 & 1 \
0 & 0 & 0 & 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ - 1 & 1 & 0 & 0 \ 7 & 7 & 1 & 0 \ - 63 & - 63 & 9 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ 9 & 1 & 0 & 0 \ 63 & 7 & 1 & 0 \ - 9 & - 7 & - 1 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c c } 1 & 9 & 63 & - 63 \ 0 & 1 & 7 & - 7 \ 0 & 0 & 1 & - 1 \ 0 & 0 & 0 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 1 & - 1 & 7 & - 63 \ 0 & 1 & 7 & - 63 \ 0 & 0 & 1 & 9 \ 0 & 0 & 0 & 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ - 1 & 1 & 0 & 0 \ 7 & 7 & 1 & 0 \ - 63 & - 63 & 9 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ 9 & 1 & 0 & 0 \ 63 & 7 & 1 & 0 \ - 9 & - 7 & - 1 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c c } 1 & 9 & 63 & - 63 \ 0 & 1 & 7 & - 7 \ 0 & 0 & 1 & - 1 \ 0 & 0 & 0 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 1 & - 1 & 7 & - 63 \ 0 & 1 & 7 & - 63 \ 0 & 0 & 1 & 9 \ 0 & 0 & 0 & 1 \end{array} \right]$

Question 8

Write the system of equations associated with the augmented matrix. Do not solve.
-$$\left[ \begin{array} { r r r | r } 
3 & 6 & 2 & - 2 \
6 & 0 & 7 & 4 \
2 & 7 & 0 & 2
\end{array} \right]$$

Accepted Answer

A)  $\left\{ \begin{array} { l } 3 x - 6 y + 2 z = - 2 \ 6 x + 7 z = - 4 \ 2 x + 7 y = - 2 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 3 x + 6 y + 2 z = - 2 \ 6 x + 7 z = 4 \ 2 x + 7 y = 2 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 3 x + 6 y + 2 z = - 2 \ 6 x + 7 z = 4 \ 2 x + 7 z = 2 \end{array} \right.$ 
A)  $\left\{ \begin{array} { l } 3 x - 6 y + 2 z = - 2 \ 6 x + 7 z = - 4 \ 2 x + 7 y = - 2 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 3 x + 6 y + 2 z = - 2 \ 6 x + 7 z = 4 \ 2 x + 7 y = 2 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 3 x + 6 y + 2 z = - 2 \ 6 x + 7 z = 4 \ 2 x + 7 z = 2 \end{array} \right.$

Question 9

Solve the system of equations.
-$$\left\{ \begin{array} { c } 
x + y + z = 7 \
x - y + 2 z = 7 \
5 x + y + z = 11
\end{array} \right.$$

Accepted Answer

A)  x = 1, y = 4, z = 2 
B)  x = 4, y = 2, z = 1 
C)  x = 1, y = 2, z = 4 
D)  x = 4, y = 1, z = 2 
A)  x = 1, y = 4, z = 2 
B)  x = 4, y = 2, z = 1 
C)  x = 1, y = 2, z = 4 
D)  x = 4, y = 1, z = 2

Question 10

Write the partial fraction decomposition of the rational expression.
-$$\frac { x + 5 } { x ^ { 3 } - 2 x ^ { 2 } + x }$$

Accepted Answer

A)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
B)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 11 } { ( x - 1 ) ^ { 2 } }$ 
C)  $\frac { - 5 } { x } + \frac { 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
D)  $\frac { 5 } { x } + \frac { 6 } { x - 1 } + \frac { - 5 } { ( x - 1 ) ^ { 2 } }$ 
A)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
B)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 11 } { ( x - 1 ) ^ { 2 } }$ 
C)  $\frac { - 5 } { x } + \frac { 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
D)  $\frac { 5 } { x } + \frac { 6 } { x - 1 } + \frac { - 5 } { ( x - 1 ) ^ { 2 } }$

Question 11

Solve the problem.
-The sum of the squares of two numbers is 5. The difference of the two numbers is 1. Find the two numbers.

Accepted Answer

A)  -2 and -1 
B)  -2 and -1; or 1 and 2 
C)  -2 and 1; or -1 and 2 
D)  1 and 2 
A)  -2 and -1 
B)  -2 and -1; or 1 and 2 
C)  -2 and 1; or -1 and 2 
D)  1 and 2

Question 12

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 113 \
x + y = 15
\end{array} \right.$$

Accepted Answer

A)  x = 8, y = 7; x = 7, y = 8 
B)  x = 8, y = -7; x = 7, y = -8 
C)  x = -8, y = 7; x = -7, y = 8 
D)  x = -8, y = -7; x = -7, y = -8 
A)  x = 8, y = 7; x = 7, y = 8 
B)  x = 8, y = -7; x = 7, y = -8 
C)  x = -8, y = 7; x = -7, y = 8 
D)  x = -8, y = -7; x = -7, y = -8

Question 13

Graph the inequality.
-$x-y>-5$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 14

Solve the problem.
-The perimeter of a rectangle is 22 inches and its area is 28 square inches. What are its dimensions?

Accepted Answer

A)  3 in. by 6 in. 
B)  4 in. by 7 in. 
C)  3 in. by 8 in. 
D)  5 in. by 6 in. 
A)  3 in. by 6 in. 
B)  4 in. by 7 in. 
C)  3 in. by 8 in. 
D)  5 in. by 6 in.

Question 15

Solve the problem.
-The sum of the squares of two numbers is 20. The sum of the two numbers is -6. Find the two numbers.

Accepted Answer

A)  -4 and -2 
B)  -2 and 4; or -4 and 2 
C)  2 and 4 
D)  -4 and -2; or 2 and 4 
A)  -4 and -2 
B)  -2 and 4; or -4 and 2 
C)  2 and 4 
D)  -4 and -2; or 2 and 4

Question 16

Write a system of linear inequalities that has the given graph.
-  A) 
$\left\{ \begin{array} { l } y \geq 0 \ y \leq 8 \ y \leq x - 5 \ y \geq 5 - x \end{array} \right.$

Accepted Answer

B) 
$\left\{ \begin{array} { l } y \geq 0 \ x \leq 8 \ y \leq x - 5 \ y \geq 5 - x \end{array} \right.$

C) 
$\left\{ \begin{array} { l } x \geq 0 \ y \geq 0 \ y \leq 8 \ y \leq x - 5 \ y \leq 5 - x \end{array} \right.$ 
D) 
$\left\{ \begin{array} { l } x \geq 0 \ y \leq 8 \ y \leq x - 5 \ y \geq 5 - x \end{array} \right.$ 
B) 
$\left\{ \begin{array} { l } y \geq 0 \ x \leq 8 \ y \leq x - 5 \ y \geq 5 - x \end{array} \right.$

C) 
$\left\{ \begin{array} { l } x \geq 0 \ y \geq 0 \ y \leq 8 \ y \leq x - 5 \ y \leq 5 - x \end{array} \right.$ 
D) 
$\left\{ \begin{array} { l } x \geq 0 \ y \leq 8 \ y \leq x - 5 \ y \geq 5 - x \end{array} \right.$

Question 17

Write the partial fraction decomposition of the rational expression.
-$$\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$$

Accepted Answer

A)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$ 
B)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$ 
C)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$ 
D)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$ 
A)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$ 
B)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$ 
C)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$ 
D)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$

Question 18

Write the word or phrase that best completes each statement or answers the question.
-Lexie wants to have an income of $9000 per year from investments. To that end she is going to invest $90,000 in
three different accounts. These accounts pay 7%, 10%, and 14% simple interest. If she wants to have $10,000
more in the account paying 7% simple interest than she has in the account paying 14% simple interest, how
much should go into each account?

Accepted Answer

$40,000 at

Question 19

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

Accepted Answer

A)  $\left[ \begin{array} { l r } 1 & 5 \ - 4 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 0 & 10 \ 0 & - 1 \ 0 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 1 & - 4 \ 5 & 9 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } 10 & - 5 & 1 \ 5 & - 1 & 0 \ - 5 & - 2 & 0 \end{array} \right]$ 
A)  $\left[ \begin{array} { l r } 1 & 5 \ - 4 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 0 & 10 \ 0 & - 1 \ 0 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 1 & - 4 \ 5 & 9 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } 10 & - 5 & 1 \ 5 & - 1 & 0 \ - 5 & - 2 & 0 \end{array} \right]$

Question 20

Graph the inequality.
-$-2 x-4 y \leq 8$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Graph the inequality. - $x-y<-2$ A) B) C) D)

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x - y = 1\end{array} \right.$

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 9 x + 8 y = 50 \\5 x + 6 y = 34\end{array} \right.$

Use the elimination method to solve the system. - $\left\{ \begin{array} { l } x + y = - 8 \\x - y = 12\end{array} \right.$

Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } 9 x - 2 y - z = 64 \\x - 3 y - 3 z = - 27 \\- 6 x + y + z = - 42\end{array} \right.$

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[ \begin{array} { r r r r } 1 & - 9 & 0 & 0 \\0 & 1 & - 7 & 0 \\0 & 0 & 1 & 1 \\0 & 0 & 0 & 1\end{array} \right]$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r | r } 3 & 6 & 2 & - 2 \\6 & 0 & 7 & 4 \\2 & 7 & 0 & 2\end{array} \right]$

Solve the system of equations. - $\left\{ \begin{array} { c } x + y + z = 7 \\x - y + 2 z = 7 \\5 x + y + z = 11\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x + 5 } { x ^ { 3 } - 2 x ^ { 2 } + x }$

Solve the problem. -The sum of the squares of two numbers is 5. The difference of the two numbers is 1. Find the two numbers.

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 113 \\x + y = 15\end{array} \right.$

Graph the inequality. - $x-y>-5$ A) B) C) D)

Solve the problem. -The perimeter of a rectangle is 22 inches and its area is 28 square inches. What are its dimensions?

Solve the problem. -The sum of the squares of two numbers is 20. The sum of the two numbers is -6. Find the two numbers.

Write the partial fraction decomposition of the rational expression. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

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

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 10: Systems of Equations and Inequalities

Graph the inequality. - x−y<−2x-y<-2x−y<−2 A) B) C) D)

Solve the system of equations using substitution. - {x2+y2=61x−y=1\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x - y = 1\end{array} \right.{x2+y2=61x−y=1​

Write the augmented matrix for the system. - {9x+8y=505x+6y=34\left\{ \begin{array} { l } 9 x + 8 y = 50 \\5 x + 6 y = 34\end{array} \right.{9x+8y=505x+6y=34​

Graph the system of inequalities. - y\geq x+y>2 A) B) C) D)

Use the elimination method to solve the system. - {x+y=−8x−y=12\left\{ \begin{array} { l } x + y = - 8 \\x - y = 12\end{array} \right.{x+y=−8x−y=12​

Use Cramer's rule to solve the linear system. - {9x−2y−z=64x−3y−3z=−27−6x+y+z=−42\left\{ \begin{array} { l } 9 x - 2 y - z = 64 \\x - 3 y - 3 z = - 27 \\- 6 x + y + z = - 42\end{array} \right.⎩⎨⎧​9x−2y−z=64x−3y−3z=−27−6x+y+z=−42​

Write the system of equations associated with the augmented matrix. Do not solve. - [362−260742702]\left[ \begin{array} { r r r | r } 3 & 6 & 2 & - 2 \\6 & 0 & 7 & 4 \\2 & 7 & 0 & 2\end{array} \right]​362​607​270​−242​​

Solve the system of equations. - {x+y+z=7x−y+2z=75x+y+z=11\left\{ \begin{array} { c } x + y + z = 7 \\x - y + 2 z = 7 \\5 x + y + z = 11\end{array} \right.⎩⎨⎧​x+y+z=7x−y+2z=75x+y+z=11​

Write the partial fraction decomposition of the rational expression. - x+5x3−2x2+x\frac { x + 5 } { x ^ { 3 } - 2 x ^ { 2 } + x }x3−2x2+xx+5​

Solve the problem. -The sum of the squares of two numbers is 5. The difference of the two numbers is 1. Find the two numbers.

Solve the system of equations using substitution. - {x2+y2=113x+y=15\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 113 \\x + y = 15\end{array} \right.{x2+y2=113x+y=15​

Graph the inequality. - x−y>−5x-y>-5x−y>−5 A) B) C) D)

Solve the problem. -The perimeter of a rectangle is 22 inches and its area is 28 square inches. What are its dimensions?

Solve the problem. -The sum of the squares of two numbers is 20. The sum of the two numbers is -6. Find the two numbers.

Write the partial fraction decomposition of the rational expression. - x2−111x4−x2−72\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }x4−x2−72x2−111​

Perform the matrix multiplication. -Let A=[0−315−10]A = \left[ \begin{array} { l l l } 0 & - 3 & 1 \\ 5 & - 1 & 0 \end{array} \right]A=[05​−3−1​10​] and B=[12011−1]B = \left[ \begin{array} { r r } 1 & 2 \\ 0 & 1 \\ 1 & - 1 \end{array} \right]B=​101​21−1​​ . Find ABA BAB .

Graph the inequality. - −2x−4y≤8-2 x-4 y \leq 8−2x−4y≤8 A) B) C) D)

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Graph the inequality. - $x-y<-2$ A) B) C) D)

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x - y = 1\end{array} \right.$

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 9 x + 8 y = 50 \\5 x + 6 y = 34\end{array} \right.$

Use the elimination method to solve the system. - $\left\{ \begin{array} { l } x + y = - 8 \\x - y = 12\end{array} \right.$

Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } 9 x - 2 y - z = 64 \\x - 3 y - 3 z = - 27 \\- 6 x + y + z = - 42\end{array} \right.$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r | r } 3 & 6 & 2 & - 2 \\6 & 0 & 7 & 4 \\2 & 7 & 0 & 2\end{array} \right]$

Solve the system of equations. - $\left\{ \begin{array} { c } x + y + z = 7 \\x - y + 2 z = 7 \\5 x + y + z = 11\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x + 5 } { x ^ { 3 } - 2 x ^ { 2 } + x }$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 113 \\x + y = 15\end{array} \right.$

Graph the inequality. - $x-y>-5$ A) B) C) D)

Write the partial fraction decomposition of the rational expression. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

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