Question 1)

Give the order of the following matrix; if A = [a_ij], identify a₃₂ and a₂₃.

Question 2

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

Question 3

If AB = -BA, then A and B are said to be anticommutative.

Question 4

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

The inverse of:

is

Question 5

Use Cramer’s Rule to solve the following system.
 

Question 6

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

Question 7

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

Question 8

Use Cramer’s Rule to solve the following system.
 

Question 9

Use Cramer’s Rule to solve the following system.

Question 10

Use Cramer’s Rule to solve the following system.

Question 11

Use Cramer’s Rule to solve the following system.

Question 12

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

Question 13

Use Cramer’s Rule to solve the following system.

Question 14

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

Question 15

Use Gauss-Jordan elimination to solve the system.

Question 16

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

Question 17

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

Question 18

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

Question 19

Use Cramer’s Rule to solve the following system.

Question 20

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

Question 21

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

y²/4 - x²/1 = 1

Question 22

Locate the foci of the ellipse of the following equation.

x²/16 + y²/4 = 1

Question 23

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

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

Question 24

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

Question 25

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 26

Locate the foci of the ellipse of the following equation.

25x² + 4y² = 100

Question 27

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 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)

Question 29

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

(y + 3)² = 12(x + 1)

Question 30

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 31

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

4x² + y² + 16x - 6y - 39 = 0

Question 32

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

Question 33

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

9x² + 16y² - 18x + 64y - 71 = 0

Question 34

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 35

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

(y + 1)² = -8x

Question 36

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

8x² + 4y = 0

Question 37

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

9x² + 25y² - 36x + 50y - 164 = 0

Question 38

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 39

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

x² = -4y

Question 40

Locate the foci and find the equations of the asymptotes.
 
x²/9 - y²/25 = 1