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9 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Linear Equation
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ax = b
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Linear Equation of n unknowns
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a1x1 + a2x2 + a3x3... anxn
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Equivalency (Systems)
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A pair of systems is equivalent when both have the same solution set.
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Consistency (Linear Equations)
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A system of linear equations is consistent if it has at least one solution.
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Co-efficience matrix
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* Each row represents an equation
* Each column represents an unknown |
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Augmented Matrix
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Same as co-efficience matrix, with an added column for the result of each equation
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Linear Independence
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None of the vectors in a set {v1... vn} can be written as a linear combination of the other vectors in the set.
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Tricks to determining dependence:
1. One of the vectors in the set is the zero vector. 2. Theorem 8. 3. Some of the vectors are scalar multiples of others. |
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Theorem 1
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Every system of linear equations can have:
* 0 solutions - if the equations are parallel * 1 solution - if all equations intersect (can only happen once) * Infinite solutions - if all equations have the same line graph |
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Theorem 8
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If there are more vectors in a set than there are entries in each vector,
The vectors are l.d. |
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