Question 1

Find the complete solution of the system. $$\left\{ \begin{array} { r } 
2 x + 3 y = 11 \
3 x + 3 y = 9 \
x + z = 1
\end{array} \right.$$

Accepted Answer

The answer of Find the complete solution of the system....

Question 2

The system is linear. $\left\{ \begin{array} { r } 
x + 2 y + z = 3 \
\sqrt { 2 } x + y - \sqrt { 3 } z = 1 \
x + y + 4 z = - 4
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 3

Determine which point is a solution for the system of inequalities. $\left\{ \begin{array} { l } 
y > 4 - x ^ { 2 } \
x ^ { 2 } + y ^ { 2 } \leq 9
\end{array} \right.$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( 0,1 )$ 
C)  $( 3,0 )$ 
D)  $( 0,3 )$ 
E)  $( 0 , - 3 )$ 
A)  $( 0,0 )$ 
B)  $( 0,1 )$ 
C)  $( 3,0 )$ 
D)  $( 0,3 )$ 
E)  $( 0 , - 3 )$

Question 4

Solve the system. $\left\{ \begin{array} { l } 
x = y ^ { 2 } \
x - y = 2
\end{array} \right.$

Accepted Answer

The answer of Solve the system. \(\left\{ \begin{array} { l...

Question 5

Gary invests a total of $\$ 21,000$  in two accounts, one paying $5.5 \%$  simple interest per year and the other paying $8.5 \%$  simple interest per year. His annual interest from both accounts is $\$ 1,280$  . How much did he invest at each rate?

Accepted Answer

The answer of Gary invests a total of $\$ 21,000$...

Question 6

Find the determinant of the matrix $\left[ \begin{array} { r r } 
\frac { 1 } { 2 } & 1 \\
- \frac { 1 } { 2 } & \frac { 3 } { 2 }
\end{array} \right]$ , if it exists

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $5$ 
C)  $- \frac { 5 } { 4 }$ 
D)  $\frac { 1 } { 4 }$ 
E)  $\frac { 5 } { 4 }$ 
A)  $\frac { 3 } { 4 }$ 
B)  $5$ 
C)  $- \frac { 5 } { 4 }$ 
D)  $\frac { 1 } { 4 }$ 
E)  $\frac { 5 } { 4 }$

Question 7

Find the determinant and, if possible, the inverse of the matrix. $$\left[ \begin{array} { l l l } 
2 & 2 & 0 \
0 & 2 & 0 \
1 & 0 & 1
\end{array} \right]$$

Accepted Answer

\[\operatorname { det } \left[ \begin{ar

Question 8

Find the complete solution of the system. $$\left\{ \begin{array} { r } 
x + y + z = 3 \
x - y + z = - 2 \
x + y + 3 z = 1
\end{array} \right.$$

Accepted Answer

The answer of Find the complete solution of the system....

Question 9

Graph the solution of the system of inequalities. $$\left\{ \begin{array} { l } 
y > 4 - x ^ { 2 } \
x ^ { 2 } + y ^ { 2 } \leq 9
\end{array} \right.$$

Accepted Answer

The answer of Graph the solution of the system of...

Question 10

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. $$\left[ \begin{array} { l l l l } 
1 & 0 & 1 & 1 \
0 & 1 & 0 & 1 \
1 & 0 & 1 & 1
\end{array} \right]$$

Accepted Answer

A) row-echelon form 
B) reduced row-echelon form 
C) neither 
A) row-echelon form 
B) reduced row-echelon form 
C) neither

Question 11

A man invests a total of $\$ 21,000$  in two accounts, one paying $5.5 \%$  simple interest per year and the other paying $8.5 \%$  simple interest per year. His annual interest from both accounts is $\$ 1,280$  . How much did he invest at each rate?

Accepted Answer

The answer of A man invests a total of \(\$...

Question 12

Determine whether the system is linear or nonlinear. $$\left\{ \begin{array} { l } 
y = 3 - 2 x \
y - 4 = 2 x
\end{array} \right.$$

Accepted Answer

The answer of Determine whether the system is linear or...

Question 13

Find the dimension of matrix A. $A = \left[ \begin{array} { l l l } 
- 1 & 2 & - 3 \
4 & - 5 & 6
\end{array} \right]$

Accepted Answer

A)  $2 \times 3$ 
B)  $2 \times 4$ 
C)  $3 \times 2$ 
D)  $1 \times 3$ 
E) none 
A)  $2 \times 3$ 
B)  $2 \times 4$ 
C)  $3 \times 2$ 
D)  $1 \times 3$ 
E) none

Question 14

Use Cramer's Rule to solve the system. $\left\{ \begin{array} { r } 
2 x - y - 3 z = 3 \
x + 3 y - 2 z = - 4 \
7 x + 7 y - 12 z = - 5
\end{array} \right.$

Accepted Answer

A)  $( 3,1,0 )$ 
B)  $( - 3 , - 1,0 )$ 
C)  $( 2,1,10 )$ 
D)  $( - 3,2,0 )$ 
E) no solution 
A)  $( 3,1,0 )$ 
B)  $( - 3 , - 1,0 )$ 
C)  $( 2,1,10 )$ 
D)  $( - 3,2,0 )$ 
E) no solution

Question 15

Solve the system. $\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 18 \
x - y = 0
\end{array} \right.$

Accepted Answer

A)  $( 2 , - 3 ) , ( - 2 , - 3 )$ 
B)  $( 2 , - 1 ) , ( 2,1 )$ 
C)  $( 3,0 ) , ( 0,3 )$ 
D)  $( - 3 , - 3 ) , ( - 2 , - 3 )$ 
E)  $( 3,3 ) , ( - 3 , - 3 )$ 
A)  $( 2 , - 3 ) , ( - 2 , - 3 )$ 
B)  $( 2 , - 1 ) , ( 2,1 )$ 
C)  $( 3,0 ) , ( 0,3 )$ 
D)  $( - 3 , - 3 ) , ( - 2 , - 3 )$ 
E)  $( 3,3 ) , ( - 3 , - 3 )$

Question 16

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. $$\left[ \begin{array} { c c c c } 
1 & 10 & 0 & 3 \
0 & 1 & 0 & 3 \
0 & 0 & 1 & 10
\end{array} \right]$$

Accepted Answer

The answer of Determine whether the matrix is in row-echelon...

Question 17

Solve the system. $\left\{ \begin{array} { l } 
y = x ^ { 2 } - 25 \
y - 5 = x
\end{array} \right.$

Accepted Answer

A)  $( - 5,0 ) , ( 5,11 )$ 
B)  $( - 5,0 ) , ( 6,11 )$ 
C)  $( - 6,11 ) , ( 6,11 )$ 
D)  $( - 5,6 ) , ( 0,11 )$ 
E)  $( 5,0 ) , ( - 6,0 )$ 
A)  $( - 5,0 ) , ( 5,11 )$ 
B)  $( - 5,0 ) , ( 6,11 )$ 
C)  $( - 6,11 ) , ( 6,11 )$ 
D)  $( - 5,6 ) , ( 0,11 )$ 
E)  $( 5,0 ) , ( - 6,0 )$

Question 18

Solve $\left[ \begin{array} { l l } 
2 & x \
6 & 0
\end{array} \right] \left[ \begin{array} { l l } 
y & 3 \
- 2 & 2
\end{array} \right] = \left[ \begin{array} { l l } 
1 & 3 \
- 6 & 18
\end{array} \right]$ for $x$
And $y$

Accepted Answer

A)  $x = - 2$, $y = - 1$ 
B)  $x = - \frac { 3 } { 2 }$, $y = - 2$ 
C)  $x = - \frac { 3 } { 2 }$, $y = - 1$ 
D)  $x = \frac { J } { 2 }$, $y = - \frac { 3 } { 2 }$ 
E)  none 
A)  $x = - 2$, $y = - 1$ 
B)  $x = - \frac { 3 } { 2 }$, $y = - 2$ 
C)  $x = - \frac { 3 } { 2 }$, $y = - 1$ 
D)  $x = \frac { J } { 2 }$, $y = - \frac { 3 } { 2 }$ 
E)  none

Question 19

Solve the system of equations $$\left\{ \begin{array} { r } 
x + 3 y - 2 z = 1 \
2 x + 4 y + z = 4 \
2 x + 6 y - z = 2
\end{array} \right.$$ by converting to a matrix equation and using its inverse coefficient matrix $\left[ \begin{array} { c c c } 
\frac { 3 } { 3 } & \frac { 3 } { 2 } & - \frac { 11 } { 6 } \
- \frac { 2 } { 3 } & - \frac { 1 } { 2 } & \frac { 3 } { 6 } \
- \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 }
\end{array} \right]$

Accepted Answer

A)  $( - 14 , - 3,0 )$ 
B)  $( 2,3,0 )$ 
C)  $( - 8,3,0 )$ 
D)  $( - 8,0,1 )$ 
E)  $( - 6 , - 3,0 )$ 
A)  $( - 14 , - 3,0 )$ 
B)  $( 2,3,0 )$ 
C)  $( - 8,3,0 )$ 
D)  $( - 8,0,1 )$ 
E)  $( - 6 , - 3,0 )$

Question 20

Find the complete solution of the system. $\left\{ \begin{array} { l } 
x + z = 4 \
y + 2 z = 1 \
- y + z = 0
\end{array} \right.$

Accepted Answer

A)  $x = \frac { 11 } { 3 }$, $y = \frac { 1 } { 3 }$, $z = \frac { 1 } { 3 }$ 
B)  $x = \frac { 11 } { 3 }$, $y = \frac { 4 } { 3 }$, $z = \frac { 1 } { 3 }$ 
C)  $x = \frac { 11 } { 3 }$, $y = \frac { 1 } { 3 }$, $z = - \frac { 2 } { 3 }$ 
D)  $x = 3$, $y = 1$, $z = 11$ 
E)  no solution 
A)  $x = \frac { 11 } { 3 }$, $y = \frac { 1 } { 3 }$, $z = \frac { 1 } { 3 }$ 
B)  $x = \frac { 11 } { 3 }$, $y = \frac { 4 } { 3 }$, $z = \frac { 1 } { 3 }$ 
C)  $x = \frac { 11 } { 3 }$, $y = \frac { 1 } { 3 }$, $z = - \frac { 2 } { 3 }$ 
D)  $x = 3$, $y = 1$, $z = 11$ 
E)  no solution

Find the complete solution of the system. $\left\{ \begin{array} { r } 2 x + 3 y = 11 \\3 x + 3 y = 9 \\x + z = 1\end{array} \right.$

The system is linear. $\left\{ \begin{array} { r } x + 2 y + z = 3 \\\sqrt { 2 } x + y - \sqrt { 3 } z = 1 \\x + y + 4 z = - 4\end{array} \right.$

Determine which point is a solution for the system of inequalities. $\left\{ \begin{array} { l } y > 4 - x ^ { 2 } \\x ^ { 2 } + y ^ { 2 } \leq 9\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x = y ^ { 2 } \\x - y = 2\end{array} \right.$

Gary invests a total of $\$ 21,000$ in two accounts, one paying $5.5 \%$ simple interest per year and the other paying $8.5 \%$ simple interest per year. His annual interest from both accounts is $\$ 1,280$ . How much did he invest at each rate?

Find the determinant of the matrix $\left[ \begin{array} { r r } \frac { 1 } { 2 } & 1 \\\\- \frac { 1 } { 2 } & \frac { 3 } { 2 }\end{array} \right]$ , if it exists

Find the determinant and, if possible, the inverse of the matrix. $\left[ \begin{array} { l l l } 2 & 2 & 0 \\0 & 2 & 0 \\1 & 0 & 1\end{array} \right]$

Find the complete solution of the system. $\left\{ \begin{array} { r } x + y + z = 3 \\x - y + z = - 2 \\x + y + 3 z = 1\end{array} \right.$

Graph the solution of the system of inequalities. $\left\{ \begin{array} { l } y > 4 - x ^ { 2 } \\x ^ { 2 } + y ^ { 2 } \leq 9\end{array} \right.$

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. $\left[ \begin{array} { l l l l } 1 & 0 & 1 & 1 \\0 & 1 & 0 & 1 \\1 & 0 & 1 & 1\end{array} \right]$

A man invests a total of $\$ 21,000$ in two accounts, one paying $5.5 \%$ simple interest per year and the other paying $8.5 \%$ simple interest per year. His annual interest from both accounts is $\$ 1,280$ . How much did he invest at each rate?

Determine whether the system is linear or nonlinear. $\left\{ \begin{array} { l } y = 3 - 2 x \\y - 4 = 2 x\end{array} \right.$

Find the dimension of matrix A. $A = \left[ \begin{array} { l l l } - 1 & 2 & - 3 \\4 & - 5 & 6\end{array} \right]$

Use Cramer's Rule to solve the system. $\left\{ \begin{array} { r } 2 x - y - 3 z = 3 \\x + 3 y - 2 z = - 4 \\7 x + 7 y - 12 z = - 5\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 18 \\x - y = 0\end{array} \right.$

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. $\left[ \begin{array} { c c c c } 1 & 10 & 0 & 3 \\0 & 1 & 0 & 3 \\0 & 0 & 1 & 10\end{array} \right]$

Solve the system. $\left\{ \begin{array} { l } y = x ^ { 2 } - 25 \\y - 5 = x\end{array} \right.$

Solve $\left[ \begin{array} { l l } 2 & x \\6 & 0\end{array} \right] \left[ \begin{array} { l l } y & 3 \\- 2 & 2\end{array} \right] = \left[ \begin{array} { l l } 1 & 3 \\- 6 & 18\end{array} \right]$ for $x$ And $y$

Find the complete solution of the system. $\left\{ \begin{array} { l } x + z = 4 \\y + 2 z = 1 \\- y + z = 0\end{array} \right.$

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 11: Matrices and Determinants

Find the complete solution of the system. {2x+3y=113x+3y=9x+z=1\left\{ \begin{array} { r } 2 x + 3 y = 11 \\3 x + 3 y = 9 \\x + z = 1\end{array} \right.⎩⎨⎧​2x+3y=113x+3y=9x+z=1​

The system is linear. {x+2y+z=32x+y−3z=1x+y+4z=−4\left\{ \begin{array} { r } x + 2 y + z = 3 \\\sqrt { 2 } x + y - \sqrt { 3 } z = 1 \\x + y + 4 z = - 4\end{array} \right.⎩⎨⎧​x+2y+z=32​x+y−3​z=1x+y+4z=−4​

Determine which point is a solution for the system of inequalities. {y>4−x2x2+y2≤9\left\{ \begin{array} { l } y > 4 - x ^ { 2 } \\x ^ { 2 } + y ^ { 2 } \leq 9\end{array} \right.{y>4−x2x2+y2≤9​

Solve the system. {x=y2x−y=2\left\{ \begin{array} { l } x = y ^ { 2 } \\x - y = 2\end{array} \right.{x=y2x−y=2​

Gary invests a total of $21,000\$ 21,000$21,000 in two accounts, one paying 5.5%5.5 \%5.5% simple interest per year and the other paying 8.5%8.5 \%8.5% simple interest per year. His annual interest from both accounts is $1,280\$ 1,280$1,280 . How much did he invest at each rate?

Find the determinant of the matrix [121−1232]\left[ \begin{array} { r r } \frac { 1 } { 2 } & 1 \\\\- \frac { 1 } { 2 } & \frac { 3 } { 2 }\end{array} \right]​21​−21​​123​​​ , if it exists

Find the determinant and, if possible, the inverse of the matrix. [220020101]\left[ \begin{array} { l l l } 2 & 2 & 0 \\0 & 2 & 0 \\1 & 0 & 1\end{array} \right]​201​220​001​​

Find the complete solution of the system. {x+y+z=3x−y+z=−2x+y+3z=1\left\{ \begin{array} { r } x + y + z = 3 \\x - y + z = - 2 \\x + y + 3 z = 1\end{array} \right.⎩⎨⎧​x+y+z=3x−y+z=−2x+y+3z=1​

Graph the solution of the system of inequalities. {y>4−x2x2+y2≤9\left\{ \begin{array} { l } y > 4 - x ^ { 2 } \\x ^ { 2 } + y ^ { 2 } \leq 9\end{array} \right.{y>4−x2x2+y2≤9​

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. [101101011011]\left[ \begin{array} { l l l l } 1 & 0 & 1 & 1 \\0 & 1 & 0 & 1 \\1 & 0 & 1 & 1\end{array} \right]​101​010​101​111​​

A man invests a total of $21,000\$ 21,000$21,000 in two accounts, one paying 5.5%5.5 \%5.5% simple interest per year and the other paying 8.5%8.5 \%8.5% simple interest per year. His annual interest from both accounts is $1,280\$ 1,280$1,280 . How much did he invest at each rate?

Determine whether the system is linear or nonlinear. {y=3−2xy−4=2x\left\{ \begin{array} { l } y = 3 - 2 x \\y - 4 = 2 x\end{array} \right.{y=3−2xy−4=2x​

Find the dimension of matrix A. A=[−12−34−56]A = \left[ \begin{array} { l l l } - 1 & 2 & - 3 \\4 & - 5 & 6\end{array} \right]A=[−14​2−5​−36​]

Use Cramer's Rule to solve the system. {2x−y−3z=3x+3y−2z=−47x+7y−12z=−5\left\{ \begin{array} { r } 2 x - y - 3 z = 3 \\x + 3 y - 2 z = - 4 \\7 x + 7 y - 12 z = - 5\end{array} \right.⎩⎨⎧​2x−y−3z=3x+3y−2z=−47x+7y−12z=−5​

Solve the system. {x2+y2=18x−y=0\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 18 \\x - y = 0\end{array} \right.{x2+y2=18x−y=0​

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. [11003010300110]\left[ \begin{array} { c c c c } 1 & 10 & 0 & 3 \\0 & 1 & 0 & 3 \\0 & 0 & 1 & 10\end{array} \right]​100​1010​001​3310​​

Solve the system. {y=x2−25y−5=x\left\{ \begin{array} { l } y = x ^ { 2 } - 25 \\y - 5 = x\end{array} \right.{y=x2−25y−5=x​

Solve [2x60][y3−22]=[13−618]\left[ \begin{array} { l l } 2 & x \\6 & 0\end{array} \right] \left[ \begin{array} { l l } y & 3 \\- 2 & 2\end{array} \right] = \left[ \begin{array} { l l } 1 & 3 \\- 6 & 18\end{array} \right][26​x0​][y−2​32​]=[1−6​318​] for xxx And yyy

Find the complete solution of the system. {x+z=4y+2z=1−y+z=0\left\{ \begin{array} { l } x + z = 4 \\y + 2 z = 1 \\- y + z = 0\end{array} \right.⎩⎨⎧​x+z=4y+2z=1−y+z=0​

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Counting and Probability

Filters

Find the complete solution of the system. $\left\{ \begin{array} { r } 2 x + 3 y = 11 \\3 x + 3 y = 9 \\x + z = 1\end{array} \right.$

The system is linear. $\left\{ \begin{array} { r } x + 2 y + z = 3 \\\sqrt { 2 } x + y - \sqrt { 3 } z = 1 \\x + y + 4 z = - 4\end{array} \right.$

Determine which point is a solution for the system of inequalities. $\left\{ \begin{array} { l } y > 4 - x ^ { 2 } \\x ^ { 2 } + y ^ { 2 } \leq 9\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x = y ^ { 2 } \\x - y = 2\end{array} \right.$

Gary invests a total of $\$ 21,000$ in two accounts, one paying $5.5 \%$ simple interest per year and the other paying $8.5 \%$ simple interest per year. His annual interest from both accounts is $\$ 1,280$ . How much did he invest at each rate?

Find the determinant of the matrix $\left[ \begin{array} { r r } \frac { 1 } { 2 } & 1 \\\\- \frac { 1 } { 2 } & \frac { 3 } { 2 }\end{array} \right]$ , if it exists

Find the determinant and, if possible, the inverse of the matrix. $\left[ \begin{array} { l l l } 2 & 2 & 0 \\0 & 2 & 0 \\1 & 0 & 1\end{array} \right]$

Find the complete solution of the system. $\left\{ \begin{array} { r } x + y + z = 3 \\x - y + z = - 2 \\x + y + 3 z = 1\end{array} \right.$

Graph the solution of the system of inequalities. $\left\{ \begin{array} { l } y > 4 - x ^ { 2 } \\x ^ { 2 } + y ^ { 2 } \leq 9\end{array} \right.$

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. $\left[ \begin{array} { l l l l } 1 & 0 & 1 & 1 \\0 & 1 & 0 & 1 \\1 & 0 & 1 & 1\end{array} \right]$

A man invests a total of $\$ 21,000$ in two accounts, one paying $5.5 \%$ simple interest per year and the other paying $8.5 \%$ simple interest per year. His annual interest from both accounts is $\$ 1,280$ . How much did he invest at each rate?

Determine whether the system is linear or nonlinear. $\left\{ \begin{array} { l } y = 3 - 2 x \\y - 4 = 2 x\end{array} \right.$

Find the dimension of matrix A. $A = \left[ \begin{array} { l l l } - 1 & 2 & - 3 \\4 & - 5 & 6\end{array} \right]$

Use Cramer's Rule to solve the system. $\left\{ \begin{array} { r } 2 x - y - 3 z = 3 \\x + 3 y - 2 z = - 4 \\7 x + 7 y - 12 z = - 5\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 18 \\x - y = 0\end{array} \right.$

Determine whether the matrix is in row-echelon form, reduced row-echelon form or neither. $\left[ \begin{array} { c c c c } 1 & 10 & 0 & 3 \\0 & 1 & 0 & 3 \\0 & 0 & 1 & 10\end{array} \right]$

Solve the system. $\left\{ \begin{array} { l } y = x ^ { 2 } - 25 \\y - 5 = x\end{array} \right.$

Solve $\left[ \begin{array} { l l } 2 & x \\6 & 0\end{array} \right] \left[ \begin{array} { l l } y & 3 \\- 2 & 2\end{array} \right] = \left[ \begin{array} { l l } 1 & 3 \\- 6 & 18\end{array} \right]$ for $x$ And $y$

Find the complete solution of the system. $\left\{ \begin{array} { l } x + z = 4 \\y + 2 z = 1 \\- y + z = 0\end{array} \right.$