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Question 1 of 40 Solve the following system of equations using matrices

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Question 1 of 40

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

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 3 of 40

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 4 of 40

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 of 40

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 6 of 40

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 7 of 40

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 8 of 40

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 9 of 40

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 10 of 40

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 11 of 40

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 of 40

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 13 of 40

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 AND D ARE SAME ANSWERS

 

A. {(-1, 2, 1, 1)}

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

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

D. {(-1, 2, 1, 1)}

Question 14 of 40

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 15 of 40

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 16 of 40

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 17 of 40

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 18 of 40

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

is

7/2 -1 0

0 1 -1

-3 0 1

 

A. {(1, 2, -1)}

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

C. {(1, 2, 0)}

D. {(1, 3, -1)}

Question 19 of 40

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 20 of 40   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 21 of 40

Locate the foci of the ellipse of the following equation.

x²/16 + y²/4 = 1

A. Foci at (-2√3, 0) and (2√3, 0)
B. Foci at (5√3, 0) and (2√3, 0)
C. Foci at (-2√3, 0) and (5√3, 0)
D. Foci at (-7√2, 0) and (5√2, 0)
Question 22 of 40

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 23 of 40   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 24 of 40   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 25 of 40

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 26 of 40   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 27 of 40   Convert each equation to standard form by completing the square on x or y. Then ?nd the vertex, focus, and directrix of the parabola. y2 - 2y + 12x - 35 = 0 B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6   C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6   D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8
Question 28 of 40

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 29 of 40

Convert each equation to standard form by completing the square on x or y. Then ?nd the vertex, focus, and directrix of the parabola.

x² - 2x - 4y + 9 = 0

 

A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1
B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3
C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1
D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5
Question 30 of 40

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 31 of 40

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 32 of 40   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 33 of 40   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 34 of 40   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 35 of 40   Convert each equation to standard form by completing the square on x and y. 4x2 + y2 + 16x - 6y - 39 = 0   A. (x + 2)2/4 + (y - 3)2/39 = 1   B. (x + 2)2/39 + (y - 4)2/64 = 1   C. (x + 2)2/16 + (y - 3)2/64 = 1   D. (x + 2)2/6 + (y - 3)2/4 = 1 Question 36 of 40   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 37 of 40   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 38 of 40           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 39 of 40   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   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