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Use Gaussian elimination with back...

Question 1 Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y + z = 4

x - y - z = 0

x - y + z = 2 A. {(3, 1, 0)} B. {(2, 1, 1)} C. {(4, 2, 1)} D. {(2, 1, 0)}

Question 2 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 3 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 5 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 6 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)}

Question7.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 8. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y - z = -2

2x - y + z = 5

-x + 2y + 2z = 1 A. {(0, -1, -2)} B. {(2, 0, 2)} C. {(1, -1, 2)} D. {(4, -1, 3)}

Question 11. 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 12. an 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 13 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 15 Use Cramer’s Rule to solve the following system.

x + y = 7

x - y = 3 A. {(7, 2)} B. {(8, -2)} C. {(5, 2)} D. {(9, 3)}

Question 16 Use Gauss-Jordan elimination to solve the system.

-x - y - z = 1

4x + 5y = 0

y - 3z = 0 A. {(14, -10, -3)} B. {(10, -2, -6)} C. {(15, -12, -4)} D. {(11, -13, -4)}

Question 17 Use Cramer’s Rule to solve the following system.

4x - 5y - 6z = -1

x - 2y - 5z = -12

2x - y = 7 A. {(2, -3, 4)} B. {(5, -7, 4)} C. {(3, -3, 3)} D. {(1, -3, 5)}

Question 18 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 19 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 21 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 22 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

Question23Find 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 24 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 25 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

x + y + z = 4

x - y - z = 0

x - y + z = 2 A. {(3, 1, 0)} B. {(2, 1, 1)} C. {(4, 2, 1)} D. {(2, 1, 0)}

Question 2 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 3 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 5 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 6 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)}

Question7.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 8. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y - z = -2

2x - y + z = 5

-x + 2y + 2z = 1 A. {(0, -1, -2)} B. {(2, 0, 2)} C. {(1, -1, 2)} D. {(4, -1, 3)}

Question 11. 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 12. an 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 13 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 15 Use Cramer’s Rule to solve the following system.

x + y = 7

x - y = 3 A. {(7, 2)} B. {(8, -2)} C. {(5, 2)} D. {(9, 3)}

Question 16 Use Gauss-Jordan elimination to solve the system.

-x - y - z = 1

4x + 5y = 0

y - 3z = 0 A. {(14, -10, -3)} B. {(10, -2, -6)} C. {(15, -12, -4)} D. {(11, -13, -4)}

Question 17 Use Cramer’s Rule to solve the following system.

4x - 5y - 6z = -1

x - 2y - 5z = -12

2x - y = 7 A. {(2, -3, 4)} B. {(5, -7, 4)} C. {(3, -3, 3)} D. {(1, -3, 5)}

Question 18 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 19 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 21 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 22 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

Question23Find 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 24 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 25 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

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