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 GaussJordan 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 GaussJordan 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 + 4×2 + 3×3 – 6×4 = 5
x1 + 3×2 + x3 – 4×4 = 3
2×1 + 8×2 + 7×3 – 5×4 = 11
2×1 + 5×2 – 6×4 = 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 = A1
C. AB = I; AB = I3; B = A1
D. AB = I3; BA = I3; A = B1
Question 11 of 40 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or GaussJordan 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 GaussJordan elimination.
3×1 + 5×2 – 8×3 + 5×4 = 8
x1 + 2×2 – 3×3 + x4 = 7
2×1 + 3×2 – 7×3 + 3×4 = 11
4×1 + 8×2 – 10×3+ 7×4 = 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 GaussJordan 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 
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)
Yintercepts: 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 
A. {(0, 2), (0, 4)} 

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

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

D. {(0, 1), (0, 1)}
Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (5, 0), (5, 0)


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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