Question: Question 1 of 40 2.5 Points Give the order of the following matrix; if A = [a ij ], identify a 32 and a 23

Question 1 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 2 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 3 of 40

2.5 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 4 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 5 of 40

2.5 Points

Use Cramers 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

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

2x + 6y + 6z = 8 2x + 7y + 6z 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 7 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 8 of 40

2.5 Points

Use Cramers 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 9 of 40

2.5 Points

Use Cramers 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 10 of 40

2.5 Points

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

A. {(1, -5, 3, 4)}

B. {(2, -1, 3, 5)}

C. {(1, 2, 3, 3)}

D. {(2, -2, 3, 4)}

Question 11 of 40

2.5 Points

Use Cramers 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 12 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 13 of 40

2.5 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 14 of 40

2.5 Points

Use Cramers 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 15 of 40

2.5 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 16 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 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.

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 18 of 40

2.5 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 19 of 40

2.5 Points

Use Cramers 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 20 of 40

2.5 Points

Use Cramers 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 21 of 40

2.5 Points

Locate the foci of the ellipse of the following equation. x2/16 + y2/4 = 1

A. Foci at (-23, 0) and (23, 0)

B. Foci at (53, 0) and (23, 0)

C. Foci at (-23, 0) and (53, 0)

D. Foci at (-72, 0) and (52, 0)

Question 22 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 23 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 24 of 40

2.5 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

Question 25 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 26 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 27 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 28 of 40

2.5 Points

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 29 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 30 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 31 of 40

2.5 Points

Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (0, -4), (0, 4) Vertices: (0, -7), (0, 7)

A. x2/43 + y2/28 = 1

B. x2/33 + y2/49 = 1

C. x2/53 + y2/21 = 1

D. x2/13 + y2/39 = 1

Question 32 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 33 of 40

2.5 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 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. 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 36 of 40

2.5 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 37 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 38 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 39 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 40 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

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