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#### 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  x1 + 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.

 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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