# Use gaussian elimination to find the complete solution to the

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 + 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 = 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.

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 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