Question 1

Transformations that are applied to augemented matrices are called elemtary row operations.

Accepted Answer

A) True 
 B)False

Question 2

Indicate whether the matrix is in reduced echelon form. $$\left. \left[ \begin{array} { c c c } 
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 0
\end{array} \right] \begin{array} { c } 
6 \
- 9\
0
\end{array} \right]$$ Enter yes or no .

Accepted Answer

The answer of Indicate whether the matrix is in reduced...

Question 3

Evaluate $2 \times 2$ determinant. $$\left| \begin{array} { c c } 
- 5 & 3 \
9 & 8
\end{array} \right|$$ Please enter your answer as a number.

Accepted Answer

The answer of Evaluate $2 \times 2$ determinant. \[\left| \begin{array}...

Question 4

A system of three linear equations in three variables produces three intersecting planes when graphed.

Accepted Answer

A) True 
 B)False

Question 5

Use a matrix approach to solve the system. $$\left( \begin{array} { c c c c } 
5 x - 4 y & = & 56 \
x + 3 y & = & - 23
\end{array} \right)$$

Accepted Answer

A)  (4, -9) 
B)  (6, -9) 
C)  (4, -8) 
D)  (6, -8) 
E)  inconsistent 
A)  (4, -9) 
B)  (6, -9) 
C)  (4, -8) 
D)  (6, -8) 
E)  inconsistent

Question 6

Solve the system by using substitution. $\left( \begin{array} { lll } 
a&=&4 b&+&6 \
2 a&+&6 b&=&-16
\end{array} \right)$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer as an ordered pair ( a , b ).

Accepted Answer

The answer of Solve the system by using substitution. \(\left(...

Question 7

The measure of the largest angle of a triangle is twice the measure of the smallest angle. The sum of the smallest angle and the largest angle is twice the other angle. Find the measure of each angle. Please enter your answer as an ordered triple ( x , y , z ), where x , y , z are the measures (in degrees) of the smallest, medium, and the largest angle, respectively. Please do not include the units in your answer.

Accepted Answer

The answer of The measure of the largest angle of...

Question 8

Evaluate $2 \times 2$ determinant. $$\left| \begin{array} { c c } 
\frac { 1 } { 2 } & \frac { 1 } { 3 } \
- 3 & - 6
\end{array} \right|$$

Accepted Answer

A)  -1 
B)  -2 
C)  8 
A)  -1 
B)  -2 
C)  8

Question 9

Solve the system. $$\left( \begin{array} { r l c c } 
2 x& - &5 y &- &5 z & = & 0 \
x & -& y &+& z & = & 11 \
- 5 x &+& 2 y &- &3 z & = & - 41
\end{array} \right)$$

Accepted Answer

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

Question 10

Evaluate $3 \times 3$ determinant. $$\left| \begin{array} { c c c } 
4 & - 3 & 5 \
0 & 5 & 3 \
3 & - 4 & - 3
\end{array} \right|$$ Use the properties of determinants to your advantage. Please enter your answer as a number.

Accepted Answer

The answer of Evaluate $3 \times 3$ determinant. \[\left| \begin{array}...

Question 11

Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l } 
x ^ { 2 } + y ^ { 2 } & = 10 \
x + y & = - 2
\end{array} \right)$$

Accepted Answer

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

Question 12

Solve the system by using substitution. $$\left( \begin{array} { l } 
y& =& \frac { 2 } { 3 } x &- &4 \
5 x &- &4 y& =& 9
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer as an ordered pair ( x , y ).

Accepted Answer

The answer of Solve the system by using substitution. \[\left(...

Question 13

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $$\left( \begin{array} { l } 
x &= &3 y& +& 3 \
x &=& - 4 y& +& 5
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer as an ordered pair ( x , y ).

Accepted Answer

The answer of Solve the system by using either the...

Question 14

Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. $$\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right|$$
-Second step

Accepted Answer

A)  $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ^ { 2 + 1 } \left| \begin{array} { l l } 
1 & 6 \
7 & 9
\end{array} \right| + ( - 4 ) ( - 1 ) ^ { 2 + 2 } \left| \begin{array} { l l } 
5 & 4 \
7 & 9
\end{array} \right| + ( 0 ) ( - 1 ) ^ { 2 + 3 } \left| \begin{array} { l l } 
5 & 4 \
1 & 6
\end{array} \right|$ 
B)  $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ( - 33 ) + ( - 4 ) ( 1 ) ( 17 ) + ( 0 ) ( - 1 ) ( 26 )$ 
C)  $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = 0 - 68 + 0 = - 68$ 
A)  $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ^ { 2 + 1 } \left| \begin{array} { l l } 
1 & 6 \
7 & 9
\end{array} \right| + ( - 4 ) ( - 1 ) ^ { 2 + 2 } \left| \begin{array} { l l } 
5 & 4 \
7 & 9
\end{array} \right| + ( 0 ) ( - 1 ) ^ { 2 + 3 } \left| \begin{array} { l l } 
5 & 4 \
1 & 6
\end{array} \right|$ 
B)  $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ( - 33 ) + ( - 4 ) ( 1 ) ( 17 ) + ( 0 ) ( - 1 ) ( 26 )$ 
C)  $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = 0 - 68 + 0 = - 68$

Question 15

Solve the system by using the elimination-by-addition method. $$\left( \begin{array} { r r r r } 
9 x &- &5 y & = & - 47 \
10 x &+& 6 y & = & - 6
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer as an ordered pair ( x , y ).

Accepted Answer

The answer of Solve the system by using the elimination-by-addition...

Question 16

Change the augmented matrix of the system to reduced echelon form and then indicate the solutions of the system. $$\left( \begin{array} { c } 
x - 5 y + 5 z = 3 \
2 x - 4 y - 14 z = 12
\end{array} \right)$$ Use k to express any real number. Enter your answer in the form ( x ( k ), y ( k ), k ).

Accepted Answer

The answer of Change the augmented matrix of the system...

Question 17

Evaluate $4 \times 4$ determinant. $$\left| \begin{array} { c c c c } 
1 & 3 & 0 & 0 \
4 & - 1 & 5 & 6 \
- 3 & 5 & 1 & 7 \
3 & - 1 & - 3 & - 4
\end{array} \right|$$ Use the properties of determinants to your advantage. Please enter your answer as a number.

Accepted Answer

The answer of Evaluate $4 \times 4$ determinant. \[\left| \begin{array}...

Question 18

Evaluate $3 \times 3$ determinant. $$\left| \begin{array} { c c c } 
1 & 4 & - 1 \
5 & 1 & 4 \
4 & 6 & 5
\end{array} \right|$$ Use the properties of determinants to your advantage.

Accepted Answer

A)  -74 
B)  -7 
C)  -81 
A)  -74 
B)  -7 
C)  -81

Question 19

Solve the homogeneous system. $$\left( \begin{array} { l } 
4 x - y + z = 0 \
5 x + 2 y + 7 z = 0 \
8 x - 9 y + z = 0
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

Accepted Answer

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

Question 20

Use the appropriate property of determinants from this section to justify the true statement. $$\left| \begin{array} { c c c } 
1 & 5 & 6 \
- 2 & 7 & 9 \
- 5 & - 1 & 2
\end{array} \right| = \left| \begin{array} { c c c } 
1 & 5 & 6 \
- 2 & 7 & 9 \
0 & 24 & 32
\end{array} \right|$$ Do not evaluate the determinants.

Accepted Answer

A)  Property number 3: If square matrix B is obtained from square matrix A by multiplying each element of any row (or column) of A by some real number k , then | B | = k | A |. 
B)  Property number 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0. 
C)  Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0. 
D)  Property number 2: If square matrix B is obtained from square matrix A by interchanging two rows (or two columns), then | B | = $-$ | A |. 
E)  Property number 4: If square matrix B is obtained from square matrix A by adding k times a row (or column) of A to another row (or column) of A , then | B | = | A |. 
A)  Property number 3: If square matrix B is obtained from square matrix A by multiplying each element of any row (or column) of A by some real number k , then | B | = k | A |. 
B)  Property number 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0. 
C)  Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0. 
D)  Property number 2: If square matrix B is obtained from square matrix A by interchanging two rows (or two columns), then | B | = $-$ | A |. 
E)  Property number 4: If square matrix B is obtained from square matrix A by adding k times a row (or column) of A to another row (or column) of A , then | B | = | A |.

Transformations that are applied to augemented matrices are called elemtary row operations.

Indicate whether the matrix is in reduced echelon form. $\left. \left[ \begin{array} { c c c } 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 0\end{array} \right] \begin{array} { c } 6 \\- 9\\0\end{array} \right]$ Enter yes or no .

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { c c } - 5 & 3 \\9 & 8\end{array} \right|$ Please enter your answer as a number.

A system of three linear equations in three variables produces three intersecting planes when graphed.

Use a matrix approach to solve the system. $\left( \begin{array} { c c c c } 5 x - 4 y & = & 56 \\x + 3 y & = & - 23\end{array} \right)$

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { c c } \frac { 1 } { 2 } & \frac { 1 } { 3 } \\- 3 & - 6\end{array} \right|$

Solve the system. $\left( \begin{array} { r l c c } 2 x& - &5 y &- &5 z & = & 0 \\x & -& y &+& z & = & 11 \\- 5 x &+& 2 y &- &3 z & = & - 41\end{array} \right)$

Evaluate $3 \times 3$ determinant. $\left| \begin{array} { c c c } 4 & - 3 & 5 \\0 & 5 & 3 \\3 & - 4 & - 3\end{array} \right|$ Use the properties of determinants to your advantage. Please enter your answer as a number.

Solve the system by the substitution or elimination method. $\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 10 \\x + y & = - 2\end{array} \right)$

Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. $\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|$ -Second step

Change the augmented matrix of the system to reduced echelon form and then indicate the solutions of the system. $\left( \begin{array} { c } x - 5 y + 5 z = 3 \\2 x - 4 y - 14 z = 12\end{array} \right)$ Use k to express any real number. Enter your answer in the form ( x ( k ), y ( k ), k ).

Evaluate $4 \times 4$ determinant. $\left| \begin{array} { c c c c } 1 & 3 & 0 & 0 \\4 & - 1 & 5 & 6 \\- 3 & 5 & 1 & 7 \\3 & - 1 & - 3 & - 4\end{array} \right|$ Use the properties of determinants to your advantage. Please enter your answer as a number.

Evaluate $3 \times 3$ determinant. $\left| \begin{array} { c c c } 1 & 4 & - 1 \\5 & 1 & 4 \\4 & 6 & 5\end{array} \right|$ Use the properties of determinants to your advantage.

Solve the homogeneous system. $\left( \begin{array} { l } 4 x - y + z = 0 \\5 x + 2 y + 7 z = 0 \\8 x - 9 y + z = 0\end{array} \right)$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Filters

Exam 15: Systems of Equations: Matrices and Determinants

Transformations that are applied to augemented matrices are called elemtary row operations.

Indicate whether the matrix is in reduced echelon form. [100010000]6−90]\left. \left[ \begin{array} { c c c } 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 0\end{array} \right] \begin{array} { c } 6 \\- 9\\0\end{array} \right]​100​010​000​​6−90​​ Enter yes or no .

Evaluate 2×22 \times 22×2 determinant. ∣−5398∣\left| \begin{array} { c c } - 5 & 3 \\9 & 8\end{array} \right|​−59​38​​ Please enter your answer as a number.

A system of three linear equations in three variables produces three intersecting planes when graphed.

Use a matrix approach to solve the system. (5x−4y=56x+3y=−23)\left( \begin{array} { c c c c } 5 x - 4 y & = & 56 \\x + 3 y & = & - 23\end{array} \right)(5x−4yx+3y​==​56−23​)

Evaluate 2×22 \times 22×2 determinant. ∣1213−3−6∣\left| \begin{array} { c c } \frac { 1 } { 2 } & \frac { 1 } { 3 } \\- 3 & - 6\end{array} \right|​21​−3​31​−6​​

Solve the system. (2x−5y−5z=0x−y+z=11−5x+2y−3z=−41)\left( \begin{array} { r l c c } 2 x& - &5 y &- &5 z & = & 0 \\x & -& y &+& z & = & 11 \\- 5 x &+& 2 y &- &3 z & = & - 41\end{array} \right)​2xx−5x​−−+​5yy2y​−+−​5zz3z​===​011−41​​

Evaluate 3×33 \times 33×3 determinant. ∣4−350533−4−3∣\left| \begin{array} { c c c } 4 & - 3 & 5 \\0 & 5 & 3 \\3 & - 4 & - 3\end{array} \right|​403​−35−4​53−3​​ Use the properties of determinants to your advantage. Please enter your answer as a number.

Solve the system by the substitution or elimination method. (x2+y2=10x+y=−2)\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 10 \\x + y & = - 2\end{array} \right)(x2+y2x+y​=10=−2​)

Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. ∣5041−46709∣\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|​517​0−40​469​​ -Second step

Evaluate 3×33 \times 33×3 determinant. ∣14−1514465∣\left| \begin{array} { c c c } 1 & 4 & - 1 \\5 & 1 & 4 \\4 & 6 & 5\end{array} \right|​154​416​−145​​ Use the properties of determinants to your advantage.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Filters

Indicate whether the matrix is in reduced echelon form. $\left. \left[ \begin{array} { c c c } 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 0\end{array} \right] \begin{array} { c } 6 \\- 9\\0\end{array} \right]$ Enter yes or no .

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { c c } - 5 & 3 \\9 & 8\end{array} \right|$ Please enter your answer as a number.

Use a matrix approach to solve the system. $\left( \begin{array} { c c c c } 5 x - 4 y & = & 56 \\x + 3 y & = & - 23\end{array} \right)$

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { c c } \frac { 1 } { 2 } & \frac { 1 } { 3 } \\- 3 & - 6\end{array} \right|$

Solve the system. $\left( \begin{array} { r l c c } 2 x& - &5 y &- &5 z & = & 0 \\x & -& y &+& z & = & 11 \\- 5 x &+& 2 y &- &3 z & = & - 41\end{array} \right)$

Evaluate $3 \times 3$ determinant. $\left| \begin{array} { c c c } 4 & - 3 & 5 \\0 & 5 & 3 \\3 & - 4 & - 3\end{array} \right|$ Use the properties of determinants to your advantage. Please enter your answer as a number.

Solve the system by the substitution or elimination method. $\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 10 \\x + y & = - 2\end{array} \right)$

Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. $\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|$ -Second step

Evaluate $3 \times 3$ determinant. $\left| \begin{array} { c c c } 1 & 4 & - 1 \\5 & 1 & 4 \\4 & 6 & 5\end{array} \right|$ Use the properties of determinants to your advantage.