Assignments: MA240 Online Exam 7

Question 1 of 40

5.0 Points

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 of 40

5.0 Points

Give the order of the following matrix; if A = [a_ij], 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 3 of 40

5.0 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 4 of 40

5.0 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 5 of 40

5.0 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 6 of 40

5.0 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 7 of 40

5.0 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 8 of 40

5.0 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 9 of 40

5.0 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 10 of 40

5.0 Points

If AB = -BA, then A and B are said to be anticommutative.

Are A =

0

1

-1

0

and B =

1

0

0

-1

anticommutative?

A. AB = -AB so they are not anticommutative.

B. AB = BA so they are anticommutative.

C. BA = -BA so they are not anticommutative.

D. AB = -BA so they are anticommutative.

Question 11 of 40

5.0 Points

Use Cramer's Rule to solve the following system.

12x + 3y = 15
2x - 3y = 13

A. {(2, -3)}

B. {(1, 3)}

C. {(3, -5)}

D. {(1, -7)}

Question 12 of 40

5.0 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 13 of 40

5.0 Points

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

2x + 3y - 5z = 15
x + 2y - z = 4

A. {(6t + 28, -7t - 6, t)}

B. {(7t + 18, -3t - 7, t)}

C. {(7t + 19, -1t - 9, t)}

D. {(4t + 29, -3t - 2, t)}

Question 14 of 40

5.0 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 15 of 40

5.0 Points

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 of 40

5.0 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 17 of 40

5.0 Points

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 18 of 40

5.0 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 19 of 40

5.0 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 20 of 40

5.0 Points

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 21 of 40

5.0 Points

Locate the foci of the ellipse of the following equation.

7x² = 35 - 5y²

A. Foci at (0, -√2) and (0, √2)

B. Foci at (0, -√1) and (0, √1)

C. Foci at (0, -√7) and (0, √7)

D. Foci at (0, -√5) and (0, √5)

Question 22 of 40

5.0 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 23 of 40

5.0 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 24 of 40

5.0 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 25 of 40

5.0 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 26 of 40

5.0 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 27 of 40

5.0 Points

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

Center: (4, -2)
Focus: (7, -2)
Vertex: (6, -2)

A. (x - 4)²/4 - (y + 2)²/5 = 1

B. (x - 4)²/7 - (y + 2)²/6 = 1

C. (x - 4)²/2 - (y + 2)²/6 = 1

D. (x - 4)²/3 - (y + 2)²/4 = 1

Question 28 of 40

5.0 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 29 of 40

5.0 Points

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

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

A. x²/4 - y²/6 = 1

B. x²/6 - y²/7 = 1

C. x²/6 - y²/7 = 1

D. x²/9 - y²/7 = 1

Question 30 of 40

5.0 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 31 of 40

5.0 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 32 of 40

5.0 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 33 of 40

5.0 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 34 of 40

5.0 Points

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

x²/4 - y²/1 =1

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

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 35 of 40

5.0 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 36 of 40

5.0 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

Question 37 of 40

5.0 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 38 of 40

5.0 Points

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

9x² + 16y² - 18x + 64y - 71 = 0

A. (x - 1)²/9 + (y + 2)²/18 = 1

B. (x - 1)²/18 + (y + 2)²/71 = 1

C. (x - 1)²/16 + (y + 2)²/9 = 1

D. (x - 1)²/64 + (y + 2)²/9 = 1

Question 39 of 40

5.0 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 40 of 40

5.0 Points

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)

A. (x - 7)²/6 + (y - 6)²/7 = 1

B. (x - 7)²/5 + (y - 6)²/6 = 1

C. (x - 7)²/4 + (y - 6)²/9 = 1

D. (x - 5)²/4 + (y - 4)²/9 = 1

MA240 Online Exam 7_10 SCORE 100 PERCENT