A+ Answers

Question 1
use Cramer’s Rule to solve the following system.
 2x = 3y + 2
 5x = 51 - 4y
D. {(7, 4)}
 
Question 2
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)}
 
Question 3

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?
D. AB = -BA so they are anticommutative.
Question 4
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
A. {(1, 2, -1)}
Question 5
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
D. {(-2t + 2, 2t + 1/2, t)}
Question 6
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
D. {(2, -2, 3, 4)}
 
Question 7
Use Cramer’s Rule to solve the following system.
 4x - 5y - 6z = -1
 x - 2y - 5z = -12
 2x - y = 7
A. {(2, -3, 4)}
 
Question 8

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 9

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
B. {(2, 1, 1)}
 Question 10
Use Cramer’s Rule to solve the following system.
 
 4x - 5y = 17
 2x + 3y = 3
A. {(3, -1)}
Question 11
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
A. {(1, 3, 2, 1)}
Question 12
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
D. {(2, -1, 1)}
Question 13

Use Cramer’s Rule to solve the following system.
   12x + 3y = 15
 2x - 3y = 13
A. {(2, -3)}
Question 14

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
B. {(-3, 4, -2)}
Question 15

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)}
Question 16
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
C. {(1, -1, 2)}
Question 17
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
C. {(5 - 2t, -2 + t, t)}
Question 18
Find values for x, y, and z so that the following matrices are equal.
            2x        z  
            y + 7    4   = 
            -10       6
            13        4 
D. x = -5; y = 6; z = 6
 
Question 19
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)}
Question 20
Use Gauss-Jordan elimination to solve the system.
 -x - y - z = 1
 4x + 5y = 0
 y - 3z = 0
C. {(15, -12, -4)}
Part 2 of 2 - Lesson 7 Questions 17.5/ 50.0 Points
Question 21
Locate the foci of the ellipse of the following equation.
 25x2 + 4y2 = 100
 
D. Foci at (0, -√21) and (0, √21)
Question 22
Locate the foci and find the equations of the asymptotes.
 
 x2/100 - y2/64 = 1
D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x
Question 23
Find the standard form of the equation of each hyperbola satisfying the given conditions.
 Foci: (0, -3), (0, 3)
 Vertices: (0, -1), (0, 1)
B. y2 - x2/8 = 1
 
Question 24
Find the vertex, focus, and directrix of each parabola with the given equation.
(x + 1)2 = -8(y + 1)
 
B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1
 
Question 25
Find the standard form of the equation of each hyperbola satisfying the given conditions.
 Foci: (-4, 0), (4, 0)
 Vertices: (-3, 0), (3, 0)
D. x2/9 - y2/7 = 1
Question 26
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)
B. x2/33 + y2/49 = 1
 
Question 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)
B. x2/64 + y2/39 = 1
Question 28
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)
C. (x - 7)2/4 + (y - 6)2/9 = 1
Question 29
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)
Question 30
Locate the foci and find the equations of the asymptotes.
 
 4y2 – x2 = 1
B. (0, ±√5/2); asymptotes: y = ±1/2x
 
Question 31
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
 
Question 32
Find the vertex, focus, and directrix of each parabola with the given equation.
 (x - 2)2 = 8(y - 1)
B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1
Question 33

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
 
Question 34

Convert each equation to standard form by completing the square on x and y.
 9x2 + 16y2 - 18x + 64y - 71 = 0
C. (x - 1)2/16 + (y + 2)2/9 = 1
Question 35

Find the focus and directrix of each parabola with the given equation.
y2 = 4x
D. Focus: (1, 0); directrix: x = -1
Question 36
Locate the foci of the ellipse of the following equation.
 
7x2 = 35 - 5y2
A. Foci at (0, -√2) and (0, √2)
Question 37

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
 
Question 38
Convert each equation to standard form by completing the square on x or y. Then find 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
Question 39
Convert each equation to standard form by completing the square on x or y. Then find 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
Question 40

Convert each equation to standard form by completing the square on x and y.
4x2 + y2 + 16x - 6y - 39 = 0
C. (x + 2)2/16 + (y - 3)2/64 = 1