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16 Cards in this Set

  • Front
  • Back
System (of Equation)
two or more equations that you solve simultaneously
Scenario #1 for solutions
The Solution
Scenario #2 for solutions
Inconsistent, No Solution

Ex: 0=1
Scenario #3 for solutions
Dependent, Infinitely many solutions

Ex: 0=0
Substitution Method
1) Solve one equation for one of the variables
2) Substitute this into the other equation
3) Solve the equation for the variable
4) Substitute this into the equation from Step 1
5) State the answer as a point
Addition Method
1) Add the equations such that one of the variables disappears.
*If necessary, multiply one or more of the equations to "fix" it
2) Substitute this into the other equation to solve
a rectangular array of elements
Dimensions (or size)
# of rows X # of columns

Ex: 1 2 3
4 5 6 2X3
Square Matrix
Same number of rows and columns
Equal Matrices
Same elements in corresponding positions.
Ex. If A=B, find x and y.
A= 2 7 B= 2 x
8 6 8 y

x=7 y=6
Add/Subtract Matrices
-Same dimensions
-add/subtract corresponding elements.
Ex: A= 8 2 B= 7 3
-1 0 2 1

A+B= 15 5 A-B= 1 -1
1 1 -3 -1
A real number multiplied by a matrix
Ex: 3A A= 1 2
3 4
3A= 3 6
9 12
Multiplication of Matrices
Check dimensions

Ex: 2X3 3X5
answer's dimensions
have to be the same
1) Multiply 1st # in 1st row by 1st # in 1st column. Multiply 2nd # in 1st row by 2nd # in 1st column.

Repeat Cycle

if the inside dimensions, aren't the same, write...
--not the same, can't be multiplied
# associated with a matrix
detA= ad-bc

Ex: A= 1 2 detA= (1x4)-(2x3)
3 4 4-6
A = 1 d -b
detA -c a
Solve using Matrices
Ex: x+2y=5
1) Write a matrix equation
1 2 x = 5
3 -1 y 8
2) Multiply by the inverse of matrix A

3)Multiply the matrices, then multiply by the scalar
4) State the answer as a point