Math 110 Review

Definitions

100

A set of equations where we are looking for the coordinate point, or set of points, that satisfy all the equations

What is a system of equations?

200

The point, or set of points,
which satisfy all the equations.

What is the solution to a system of equations?

300

A system that has infinitely many
solutions.

What is a dependent system?

400

A system with no solutions.

What is an inconsistent system?

500

A system of equations with exactly one
solution. This is the
coordinate point where
the lines intersect.

What is an independent system?

Row Operations

100

E₁ 2x + 3y = 4
E₂ 3x - y = 5

E₂ + E₁

What is 5x + 2y = 9?

200

E₁ 2x + 3y = 4
E₂ 3x - y = 5

E₂ - E₁

What is x - 4y = 1?

300

E₁ 2x + 3y = 4
E₂ 3x - y = 5

3E₁

What is 6x + 9y = 12?

400

E₁ 2x + 3y = 4
E₂ 3x - y = 5

3E₁ + 2E₂

What is 12x + 7y = 2?

500

E₁ 2x + 3y = 4
E₂ 3x - y = 5

2E₁ -  3E₂

What is -5x + 9y = -7?

Systems of Equations

100

The solution to 

4x + 2y = 4

x = -1

What is (-1, 4)?

200

Triangularized version of 

x + 3y = 5

-x + 3y = 6

What is

x + 3y = 5

6y = 11

300

Solution to the system of equations

x = 2

3x + y = 4

What is (2, -2)

400

Solutions to

x + 2y = 5

2x + 4y = 15

What is none?

500

Solutions to

x + 2y - z = 10

2y + 2z = 10

z = -2

What is (-6 ,7 ,-2)?

Matrix Operations

100

A = 1   2         B =  2  5

      3   4                3  7

2A

What is 

2   4

6   8?

200

A = 1   2         B =  2  5

      3   4                3  7

A + B

What is 

3  7

6  11

300

A = 1   2         B =  2  5

      3   4                3  7

2A + B

What is

4  9

9  15?

400

A = 1   2         B =  2  5

      3   4                3  7

A - B

What is

-1  -3

0   -3?

500

A = 1   2         B =  2  5

      3   4                3  7

A x B

What is

8    19

18  43?