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### 16 Cards in this Set

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 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 A-B= 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 ad-bc detA= ad-bc Ex: A= 1 2 detA= (1x4)-(2x3) 3 4 4-6 =-2 Inverse A = 1 d -b detA -c a Solve using Matrices Ex: x+2y=5 3x-y=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