Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

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Question 1 of 40 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 
2w + x - y = 3 
w - 3x + 2y = -4 
3w + x - 3y + z = 1 
w + 2x - 4y - z = -2


A. {(1, 3, 2, 1)}

B. {(1, 4, 3, -1)}

C. {(1, 5, 1, 1)}

D. {(-1, 2, -2, 1)}
Question 2 of 40 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 
x + 2y = z - 1 
x = 4 + y - z 
x + y - 3z = -2


A. {(3, -1, 0)}

B. {(2, -1, 0)}

C. {(3, -2, 1)}

D. {(2, -1, 1)}
Question 3 of 40 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 
x + 3y = 0 
x + y + z = 1 
3x - y - z = 11


A. {(3, -1, -1)}

B. {(2, -3, -1)}

C. {(2, -2, -4)}

D. {(2, 0, -1)}
Question 4 of 40 2.5 Points
Find values for x, y, and z so that the following matrices are equal.
2x 

z y + 7 

4 = -10

6 13

4


A. x = -7; y = 6; z = 2

B. x = 5; y = -6; z = 2

C. x = -3; y = 4; z = 6

D. x = -5; y = 6; z = 6
Question 5 of 40 2.5 Points
Use Cramer’s Rule to solve the following system.
x + y + z = 0 
2x - y + z = -1 
-x + 3y - z = -8


A. {(-1, -3, 7)}

B. {(-6, -2, 4)}

C. {(-5, -2, 7)}

D. {(-4, -1, 7)}
Question 6 of 40 2.5 Points
Use Cramer’s Rule to solve the following system.

x + 2y = 3 
3x - 4y = 4


A. {(3, 1/5)}

B. {(5, 1/3)}

C. {(1, 1/2)}

D. {(2, 1/2)}
Question 7 of 40 2.5 Points
Use Cramer’s Rule to solve the following system.
3x - 4y = 4 
2x + 2y = 12


A. {(3, 1)}

B. {(4, 2)}

C. {(5, 1)}

D. {(2, 1)}
Question 8 of 40 2.5 Points
Use Gaussian elimination to find the complete solution to each system.
x1 + 4x2 + 3x3 - 6x4 = 5 
x1 + 3x2 + x3 - 4x4 = 3 
2x1 + 8x2 + 7x3 - 5x4 = 11 
2x1 + 5x2 - 6x4 = 4


A. {(-47t + 4, 12t, 7t + 1, t)}

B. {(-37t + 2, 16t, -7t + 1, t)}

C. {(-35t + 3, 16t, -6t + 1, t)}

D. {(-27t + 2, 17t, -7t + 1, t)}
Question 9 of 40 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 
w - 2x - y - 3z = -9 
w + x - y = 0 
3w + 4x + z = 6 
2x - 2y + z = 3


A. {(-1, 2, 1, 1)}

B. {(-2, 2, 0, 1)}

C. {(0, 1, 1, 3)}

D. {(-1, 2, 1, 1)}

Question 10 of 40 2.5 Points
Find the products AB and BA to determine whether B is the multiplicative inverse of A. 
A = 0

0

1 1

0

0 0

1

0

B = 0

1

0 0

0

1 1

0

0


A. AB = I; BA = I3; B = A

B. AB = I3; BA = I3; B = A-1

C. AB = I; AB = I3; B = A-1

D. AB = I3; BA = I3; A = B-1

Question 11 of 40 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 
2x - y - z = 4 
x + y - 5z = -4 
x - 2y = 4


A. {(2, -1, 1)}

B. {(-2, -3, 0)}

C. {(3, -1, 2)}

D. {(3, -1, 0)}
Question 12 of 40 2.5 Points
Use Cramer’s Rule to solve the following system.
2x = 3y + 2 
5x = 51 - 4y


A. {(8, 2)}

B. {(3, -4)}

C. {(2, 5)}

D. {(7, 4)}

Question 13 of 40 2.5 Points
Use Gaussian elimination to find the complete solution to each system.
x - 3y + z = 1 
-2x + y + 3z = -7 
x - 4y + 2z = 0


A. {(2t + 4, t + 1, t)}

B. {(2t + 5, t + 2, t)}

C. {(1t + 3, t + 2, t)}

D. {(3t + 3, t + 1, t)}

Question 14 of 40 2.5 Points
Use Cramer’s Rule to solve the following system.
x + 2y + 2z = 5 
2x + 4y + 7z = 19 
-2x - 5y - 2z = 8


A. {(33, -11, 4)}

B. {(13, 12, -3)}

C. {(23, -12, 3)}

D. {(13, -14, 3)}

Question 15 of 40 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 
5x + 8y - 6z = 14 
3x + 4y - 2z = 8 
x + 2y - 2z = 3


A. {(-4t + 2, 2t + 1/2, t)}

B. {(-3t + 1, 5t + 1/3, t)}

C. {(2t + -2, t + 1/2, t)}

D. {(-2t + 2, 2t + 1/2, t)}

Question 16 of 40 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

3x1 + 5x2 - 8x3 + 5x4 = -8
x1 + 2x2 - 3x3 + x4 = -7 
2x1 + 3x2 - 7x3 + 3x4 = -11 
4x1 + 8x2 - 10x3+ 7x4 = -10


A. {(1, -5, 3, 4)}

B. {(2, -1, 3, 5)}

C. {(1, 2, 3, 3)}

D. {(2, -2, 3, 4)}
Question 17 of 40 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 
3x + 4y + 2z = 3 
4x - 2y - 8z = -4 
x + y - z = 3


A. {(-2, 1, 2)}

B. {(-3, 4, -2)}

C. {(5, -4, -2)}

D. {(-2, 0, -1)}
Question 18 of 40 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
x - 2y + z = 0 
y - 3z = -1 
2y + 5z = -2


A. {(-1, -2, 0)}

B. {(-2, -1, 0)}

C. {(-5, -3, 0)}

D. {(-3, 0, 0)}

Question 19 of 40


2.5 Points

 

Give the order of the following matrix; if A = [aij], identify a32 and a23.





1

0

-2


-5

7

1/2


∏

-6

11


e

-∏

-1/5

 

 

 

 




 


A. 3 * 4; a32 = 1/45; a23 = 6


 


B. 3 * 4; a32 = 1/2; a23 = -6


 


C. 3 * 2; a32 = 1/3; a23 = -5


 


D. 2 * 3; a32 = 1/4; a23 = 4


Question 20 of 40


2.5 Points

 

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.









8x + 5y + 11z = 30 
-x - 4y + 2z = 3 
2x - y + 5z = 12

 

 

 

 

 

 

A. {(3 - 3t, 2 + t, t)}

 

B. {(6 - 3t, 2 + t, t)}

 


C. {(5 - 2t, -2 + t, t)}

 

D. {(2 - 1t, -4 + t, t)}


Question 21 of 40


2.5 Points

 

Find the focus and directrix of the parabola with the given equation.

8x2 + 4y = 0

 

 
















 


A. Focus: (0, -1/4); directrix: y = 1/4


 


B. Focus: (0, -1/6); directrix: y = 1/6


 


C. Focus: (0, -1/8); directrix: y = 1/8


 


D. Focus: (0, -1/2); directrix: y = 1/2


Question 22 of 40


2.5 Points

 

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Foci: (0, -3), (0, 3)
Vertices: (0, -1), (0, 1)

 

 






















 


A. y2 - x2/4 = 0


 


B. y2 - x2/8 = 1


 


C. y2 - x2/3 = 1


 


D. y2 - x2/2 = 0


Question 23 of 40


2.5 Points

 

Convert each equation to standard form by completing the square on x and y.

9x2 + 25y2 - 36x + 50y - 164 = 0

 

 



















 


A. (x - 2)2/25 + (y + 1)2/9 = 1


 


B. (x - 2)2/24 + (y + 1)2/36 = 1


 


C. (x - 2)2/35 + (y + 1)2/25 = 1


 


D. (x - 2)2/22 + (y + 1)2/50 = 1


Question 24 of 40


2.5 Points

 

Locate the foci of the ellipse of the following equation.

25x2 + 4y2 = 100

 

 





















A. Foci at (1, -√11) and (1, √11)


 


B. Foci at (0, -√25) and (0, √25)


 


C. Foci at (0, -√22) and (0, √22)


 


D. Foci at (0, -√21) and (0, √21)


Question 25 of 40


2.5 Points

 

Find the standard form of the equation of the ellipse satisfying the given conditions.

Major axis vertical with length = 10
Length of minor axis = 4
Center: (-2, 3)

 

 






















 


A. (x + 2)2/4 + (y - 3)2/25 = 1


 


B. (x + 4)2/4 + (y - 2)2/25 = 1


 


C. (x + 3)2/4 + (y - 2)2/25 = 1


 


D. (x + 5)2/4 + (y - 2)2/25 = 1


Question 26 of 40


2.5 Points

 

Find the vertices and locate the foci of each hyperbola with the given equation.

y2/4 - x2/1 = 1

 

 






















 


A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)


 


B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)


 


C.


Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)


 


D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)


Question 27 of 40


2.5 Points

 

Find the vertex, focus, and directrix of each parabola with the given equation.

(x + 1)2 = -8(y + 1)

 

 






















 


A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1


 


B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1


 


C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1


 


D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1


 


Question 28 of 40


2.5 Points

 

Find the focus and directrix of each parabola with the given equation.

y2 = 4x

 

 






















 


A. Focus: (2, 0); directrix: x = -1


 


B. Focus: (3, 0); directrix: x = -1


 


C. Focus: (5, 0); directrix: x = -1


 


D. Focus: (1, 0); directrix: x = -1


Question 29 of 40


2.5 Points

 

Locate the foci and find the equations of the asymptotes.

x2/100 - y2/64 = 1

 

 






















 


A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x


 


B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x


 


C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x


 


D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x


Question 30 of 40


2.5 Points

 

Find the vertex, focus, and directrix of each parabola with the given equation.

(y + 3)2 = 12(x + 1)

 

 






















 


A. Vertex: (-1, -3); focus: (1, -3); directrix: x = -3


 


B. Vertex: (-1, -1); focus: (4, -3); directrix: x = -5


 


C. Vertex: (-2, -3); focus: (2, -4); directrix: x = -7


 


D. Vertex: (-1, -3); focus: (2, -3); directrix: x = -4


Question 31 of 40


2.5 Points

 

Find the focus and directrix of each parabola with the given equation.

x2 = -4y

 

 






















 


A. Focus: (0, -1), directrix: y = 1


 


B. Focus: (0, -2), directrix: y = 1


 


C. Focus: (0, -4), directrix: y = 1


 


D. Focus: (0, -1), directrix: y = 2


Question 32 of 40


2.5 Points

 

Find the vertex, focus, and directrix of each parabola with the given equation.

(x - 2)2 = 8(y - 1)

 

 






















 


A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1


 


B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1


 


C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1


 


D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1


Question 33 of 40


2.5 Points

 

Locate the foci and find the equations of the asymptotes.

x2/9 - y2/25 = 1

 

 






















 


A. Foci: ({±√36, 0) ;asymptotes: y = ±5/3x


 


B. Foci: ({±√38, 0) ;asymptotes: y = ±5/3x


 


C. Foci: ({±√34, 0) ;asymptotes: y = ±5/3x


 


D. Foci: ({±√54, 0) ;asymptotes: y = ±6/3x


Question 34 of 40


2.5 Points

 

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Endpoints of transverse axis: (0, -6), (0, 6)
Asymptote: y = 2x

 

 






















 


A. y2/6 - x2/9 = 1


 


B. y2/36 - x2/9 = 1


 


C. y2/37 - x2/27 = 1


 


D. y2/9 - x2/6 = 1


Question 35 of 40


2.5 Points

 

Find the vertices and locate the foci of each hyperbola with the given equation.

x2/4 - y2/1 =1

 

 






















 


A.


Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)


 


B.


Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)


 


C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)


 


D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)


Question 36 of 40


2.5 Points

 

Find the standard form of the equation of the following ellipse satisfying the given conditions. 

Foci: (-2, 0), (2, 0)
Y-intercepts: -3 and 3

 

 






















 


A. x2/23 + y2/6 = 1


 


B. x2/24 + y2/2 = 1


 


C. x2/13 + y2/9 = 1


 


D. x2/28 + y2/19 = 1


Question 37 of 40


2.5 Points

 

Find the vertex, focus, and directrix of each parabola with the given equation.

(y + 1)2 = -8x

 

 






















 


A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2


 


B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3


 


C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1


 


D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5


Question 38 of 40


2.5 Points

 

Find the solution set for each system by finding points of intersection.









x2 + y2 = 1 
x2 + 9y = 9

 

 

 

 






















 


A. {(0, -2), (0, 4)}


 


B. {(0, -2), (0, 1)}


 


C. {(0, -3), (0, 1)}


 


D. {(0, -1), (0, 1)}










Question 39 of 40


2.5 Points


Find the standard form of the equation of the following ellipse satisfying the given conditions. 

Foci: (-5, 0), (5, 0)
Vertices: (-8, 0), (8, 0)


 


















 


A. x2/49 + y2/ 25 = 1


 


B. x2/64 + y2/39 = 1


 


C. x2/56 + y2/29 = 1


 


D. x2/36 + y2/27 = 1


Question 40 of 40


2.5 Points

 

Locate the foci and find the equations of the asymptotes.

4y2 – x2 = 1

 

 


















 


A. (0, ±√4/2); asymptotes: y = ±1/3x


 


B. (0, ±√5/2); asymptotes: y = ±1/2x


 


C. (0, ±√5/4); asymptotes: y = ±1/3x


 


D. (0, ±√5/3); asymptotes: y = ±1/2x




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