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The current answers are incorrect and I need the corrected answers.

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1. 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

[removed] A. {(-1, -2, 0)}
[removed] B. {(-2, -1, 0)}
[removed] C. {(-5, -3, 0)}
[removed] D. {(-3, 0, 0)}

2. 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

[removed] A. {(2, -1, 1)}
[removed] B. {(-2, -3, 0)}
[removed] C. {(3, -1, 2)}
[removed] D. {(3, -1, 0)}

3. 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

[removed]

A. AB = I; BA = I₃; B = A

[removed]

B. AB = I₃; BA = I₃; B = A^-1

[removed]

C. AB = I; AB = I₃; B = A^-1

[removed]

D. AB = I₃; BA = I₃; A = B^-1

4. Use Cramer’s Rule to solve the following system.

2x = 3y + 2
5x = 51 - 4y

[removed]

A. {(8, 2)}

[removed]

B. {(3, -4)}

[removed]

C. {(2, 5)}

[removed]

D. {(7, 4)}

5. 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

[removed] A. {(1, 3, 2, 1)}
[removed] B. {(1, 4, 3, -1)}
[removed] C. {(1, 5, 1, 1)}
[removed] D. {(-1, 2, -2, 1)}

6. 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

[removed] A. {(3, -1, 0)}
[removed] B. {(2, -1, 0)}
[removed] C. {(3, -2, 1)}
[removed] D. {(2, -1, 1)}

7. Use Gauss-Jordan elimination to solve the system.

-x - y - z = 1
4x + 5y = 0
y - 3z = 0

[removed] A. {(14, -10, -3)}
[removed] B. {(10, -2, -6)}
[removed] C. {(15, -12, -4)}
[removed] D. {(11, -13, -4)}

8. 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

[removed] A. {(-1, 2, 1, 1)}
[removed] B. {(-2, 2, 0, 1)}
[removed] C. {(0, 1, 1, 3)}
[removed] D. {(-1, 2, 1, 1)}

9. 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

[removed] A. {(3 - 3t, 2 + t, t)}
[removed] B. {(6 - 3t, 2 + t, t)}
[removed] C. {(5 - 2t, -2 + t, t)}
[removed] D. {(2 - 1t, -4 + t, t)}

10. 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

[removed] A. {(3, 1, 0)}
[removed] B. {(2, 1, 1)}
[removed] C. {(4, 2, 1)}
[removed] D. {(2, 1, 0)}

11. Use Cramer’s Rule to solve the following system.

x + y = 7
x - y = 3

[removed] A. {(7, 2)}
[removed] B. {(8, -2)}
[removed] C. {(5, 2)}
[removed] D. {(9, 3)}

12. 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

[removed] A. {(1, -5, 3, 4)}
[removed] B. {(2, -1, 3, 5)}
[removed] C. {(1, 2, 3, 3)}
[removed] D. {(2, -2, 3, 4)}

13. Use Cramer’s Rule to solve the following system.

4x - 5y = 17
2x + 3y = 3

[removed] A. {(3, -1)}
[removed] B. {(2, -1)}
[removed] C. {(3, -7)}
[removed] D. {(2, 0)}

14. Use Gaussian elimination to find the complete solution to each system.

x - 3y + z = 1
-2x + y + 3z = -7
x - 4y + 2z = 0

[removed] A. {(2t + 4, t + 1, t)}
[removed] B. {(2t + 5, t + 2, t)}
[removed] C. {(1t + 3, t + 2, t)}
[removed] D. {(3t + 3, t + 1, t)}

15. 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

[removed] A. {(-4t + 2, 2t + 1/2, t)}
[removed] B. {(-3t + 1, 5t + 1/3, t)}
[removed] C. {(2t + -2, t + 1/2, t)}
[removed] D. {(-2t + 2, 2t + 1/2, t)}

16. Solve the system using the inverse that is given for the coefficient matrix.

2x + 6y + 6z = 8
2x + 7y + 6z =10
2x + 7y + 7z = 9

The inverse of:

2

2

2

6

7

7

6

6

7

7/2

-1

0

0

1

-1

-3

0

1

[removed] A. {(1, 2, -1)}
[removed] B. {(2, 1, -1)}
[removed] C. {(1, 2, 0)}
[removed] D. {(1, 3, -1)}

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

4x - 5y - 6z = -1
x - 2y - 5z = -12
2x - y = 7

[removed] A. {(2, -3, 4)}
[removed] B. {(5, -7, 4)}
[removed] C. {(3, -3, 3)}
[removed] D. {(1, -3, 5)}

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

x² + y² = 1
x² + 9y = 9

[removed]

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

[removed]

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

[removed]

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

[removed]

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

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

Endpoints of major axis: (7, 9) and (7, 3)
Endpoints of minor axis: (5, 6) and (9, 6)

[removed] A. (x - 7)²/6 + (y - 6)²/7 = 1
[removed] B. (x - 7)²/5 + (y - 6)²/6 = 1
[removed] C. (x - 7)²/4 + (y - 6)²/9 = 1
[removed] D. (x - 5)²/4 + (y - 4)²/9 = 1

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

(x + 1)² = -8(y + 1)

[removed] A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1
[removed] B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1
[removed] C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1
[removed] D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1

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

(x + 1)² = -8(y + 1)

[removed] A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1
[removed] B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1
[removed] C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1
[removed] D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1

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

Foci: (-4, 0), (4, 0)
Vertices: (-3, 0), (3, 0)

[removed] A. x²/4 - y²/6 = 1
[removed] B. x²/6 - y²/7 = 1
[removed] C. x²/6 - y²/7 = 1
[removed] D. x²/9 - y²/7 = 1

23. Locate the foci of the ellipse of the following equation.

x²/16 + y²/4 = 1

[removed] A. Foci at (-2√3, 0) and (2√3, 0)
[removed] B. Foci at (5√3, 0) and (2√3, 0)
[removed] C. Foci at (-2√3, 0) and (5√3, 0)
[removed] D. Foci at (-7√2, 0) and (5√2, 0)

24. Locate the foci and find the equations of the asymptotes.

x²/9 - y²/25 = 1

[removed] A. Foci: ({±√36, 0) ;asymptotes: y = ±5/3x
[removed] B. Foci: ({±√38, 0) ;asymptotes: y = ±5/3x
[removed] C. Foci: ({±√34, 0) ;asymptotes: y = ±5/3x
[removed] D. Foci: ({±√54, 0) ;asymptotes: y = ±6/3x

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

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

[removed] A. y² - x²/4 = 0
[removed] B. y² - x²/8 = 1
[removed] C. y² - x²/3 = 1
[removed] D. y² - x²/2 = 0

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

4x² + y² + 16x - 6y - 39 = 0

[removed] A. (x + 2)²/4 + (y - 3)²/39 = 1
[removed] B. (x + 2)²/39 + (y - 4)²/64 = 1
[removed] C. (x + 2)²/16 + (y - 3)²/64 = 1
[removed] D. (x + 2)²/6 + (y - 3)²/4 = 1

27. 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)

[removed] A. x²/49 + y²/ 25 = 1
[removed] B. x²/64 + y²/39 = 1
[removed] C. x²/56 + y²/29 = 1
[removed] D. x²/36 + y²/27 = 1

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

x² = -4y

[removed] A. Focus: (0, -1), directrix: y = 1
[removed] B. Focus: (0, -2), directrix: y = 1
[removed] C. Focus: (0, -4), directrix: y = 1
[removed] D. Focus: (0, -1), directrix: y = 2

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

(y + 1)² = -8x

[removed] A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2
[removed] B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3
[removed] C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1
[removed] D. Vertex: (0, -3); focus: (-2, -1); directr