9-4 Determinants and Cramer

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9-4 Determinants and Cramers Rule
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This is a great method.

• Cramers Rule is a neat way to evaluate systems
  and if you put the work in now youll do fine.
  It can be used for any size (2 by 2, 3 by 3 or
  even larger) system.
• It is easy to memorize and fast.
• Im going to show you where Cramers Rule comes
  from but first, some definitions

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Definitions

• Determinant a square array
• 2nd Order Determinant a 2 by 2 array
• 3rd Order Determinant a 3 by 3 array
• Elements The things in the array

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What does a determinant look like?

• A 2nd order determinant looks like this
• And the value of the determinant
• Diagonal down right diagonal down left

ae
bd
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Examples

• Evaluate
• 1.
• 2.

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Why is this useful for systems?

• Lets work through an elimination example using
  all variables then we can see how the
  determinant will be useful in solving.
• Just follow you dont need to write it down.

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Lets eliminate y
Look familiar?
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If you apply the same process but eliminate x

• So, what does Cramers Rule say?

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Cramers Rule

• Given a system
• What do you think is the trick?

Replace solutions in y column to solve for y
Replace solutions in x column to solve for x
Denominators are coefficient deterimanants
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Examples

• Solve using Cramers Rule
• 1.
• 2.