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Homework answers / question archive / Question1) Use Cramer’s Rule to solve the following system

Question1) Use Cramer’s Rule to solve the following system

Math

Question1)

Use Cramer’s Rule to solve the following system.

 

x + y + z = 0 
2x - y + z = -1 
-x + 3y - z = -8

 

 

 

 
 
 
 

Question 2

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

 

 

 

 

 
 
 
 

Question 3

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

 

 

 

 
 
 
 

Question 4

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

 

 

 

 
 
 
 

Question 5

Use Cramer’s Rule to solve the following system.

 

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

 

 

 

 
 
 
 

Question 6

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

 

 

 

 
 
 
 

Question 7

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

 

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

 

 

 

 
 
 
 

Question 8

Use Cramer’s Rule to solve the following system.
 

 

x + y = 7 
x - y = 3

 

 

 

 
 
 
 

Question 9

Use Gauss-Jordan elimination to solve the system.

 

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

 

 

 

 
 
 
 

Question 10

Use Cramer’s Rule to solve the following system.
 

 

4x - 5y = 17 
2x + 3y = 3

 

 

 

 
 
 
 

Question 11

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

 

 

 

 
 
 
 

Question 12

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

 

 

 

 
 
 
 

Question 13

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

 

x1 + 4x2 + 3x3 - 6x4 = 5 
x+ 3x2 + x3 - 4x4 = 3 
2x1 + 8x2 + 7x3 - 5x4 = 11 
2x1 + 5x2 - 6x4 = 4

 

 

 

 
 
 
 

Question 14

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

 

 

 

 

 
 
 
 

Question 15

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

 

 

 

 
 
 
 

Question 16

Use Cramer’s Rule to solve the following system.

 

3x - 4y = 4 
2x + 2y = 12

 

 

 

 
 
 
 

Question 17

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?

 

 

 

 
 
 
 

Question 18

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

 

 

 

 
 
 
 

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

 

 

 

 
 
 
 

Question 20

Use Cramer’s Rule to solve the following system.
 

https://study.ashworthcollege.edu/access/content/group/ddef570e-fc7d-4cb1-bd6e-3d3f5ab3f21b/v9/Images/Exam%20Images/Lesson%202/Lesson%202%20Exam%20Question%2010.JPG

x + 2y = 3 
3x - 4y = 4

 

 

 

 
 
 
 
 

 

Question 21

Locate the foci and find the equations of the asymptotes.
 
4y2 – x2 = 1

 

 

 
 
 
 

Question 22

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)

 

 

 
 
 
 

Question 23

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

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

 

 

 
 
 
 

Question 24

Locate the foci of the ellipse of the following equation.

x2/16 + y2/4 = 1

 

 

 
 
 
 

Question 25

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

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

 

 

 
 
 
 

Question 26

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

 

 

 
 
 
 

Question 27

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

(x + 1)2 = -8(y + 1)

 

 

 
 
 
 

Question 28

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

 

 

 
 
 
 

Question 29

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

y2 = 4x

 

 

 
 
 
 

Question 30

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

(y + 1)2 = -8x

 

 

 
 
 
 

Question 31

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

4x2 + y2 + 16x - 6y - 39 = 0

 

 

 
 
 
 

Question 32

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

y2/4 - x2/1 = 1

 

 

 
 
 
 

Question 33

Locate the foci and find the equations of the asymptotes.
 
x2/100 - y2/64 = 1

 

 

 
 
 
 

Question 34

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)

 

 

 
 
 
 

Question 35

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

 

 

 
 
 
 

Question 36

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

8x2 + 4y = 0

 

 

 
 
 
 

Question 37

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

x2 = -4y

 

 

 
 
 
 

Question 38

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

 

 

 
 
 
 

Question 39

Locate the foci of the ellipse of the following equation.

25x2 + 4y2 = 100

 

 

 
 
 
 

Question 40

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

x2/4 - y2/1 =1

 

 

 
 
 
 

 

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