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16 Cards in this Set
- Front
- Back
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System (of Equation)
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two or more equations that you solve simultaneously
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Scenario #1 for solutions
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The Solution
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Scenario #2 for solutions
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Inconsistent, No Solution
Ex: 0=1 |
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Scenario #3 for solutions
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Dependent, Infinitely many solutions
Ex: 0=0 |
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Substitution Method
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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 |
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Addition Method
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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 |
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Matrix
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a rectangular array of elements
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Dimensions (or size)
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# of rows X # of columns
Ex: 1 2 3 4 5 6 2X3 |
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Square Matrix
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Same number of rows and columns
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Equal Matrices
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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 |
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Add/Subtract Matrices
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-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 |
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Scalar
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A real number multiplied by a matrix
Ex: 3A A= 1 2 3 4 3A= 3 6 9 12 |
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Multiplication of Matrices
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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 |
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Determinent
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# associated with a matrix
ad-bc detA= ad-bc Ex: A= 1 2 detA= (1x4)-(2x3) 3 4 4-6 =-2 |
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Inverse
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A = 1 d -b
detA -c a |
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Solve using Matrices
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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 |
