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16 Cards in this Set
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 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 

Matrix

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 AB= 1 1 1 1 3 1 

Scalar

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. ADD TOGETHER Repeat Cycle if the inside dimensions, aren't the same, write... not the same, can't be multiplied 

Determinent

# associated with a matrix
adbc detA= adbc Ex: A= 1 2 detA= (1x4)(2x3) 3 4 46 =2 

Inverse

A = 1 d b
detA c a 

Solve using Matrices

Ex: x+2y=5
3xy=8 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 