Finding the Inverse of a Matrix

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Finding the Inverse of a Matrix
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You can only find the inverse of a square matrix
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Finding the inverse of a 2x2 matrix

• Given a 2x2 matrix
• Find the inverse of

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What must be true?
If the formula for finding the inverse of a 2x2
matrix is
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• What happens when you multiply the inverse you
  just found by the original matrix?
• The answer your got is called the identity matrix
• All identity matrices are square and they can be
  as big or as small as you want them to be.
• Identity matrices have 1s along one of the
  diagonals and zeros everywhere else.

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Create I5x5
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Finding the inverse of any other square matrix

• Just use your calculator ?

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Solving a matrix equation

• Given the matrix equation
• You solve for X
• You must multiply in that order
• Solve the matrix equation below

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Writing a linear system as a matrix equation

• Given a linear system
• You can write the system as a matrix equation by
  placing the coefficients in matrix A, the
  variables in matrix X and the constants in matrix
  B
• The system above becomes

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Solve the following system using a matrix equation
This translates to the point (2,2) as your
solution
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Try this one
Did you get the point (1, -2,4)??
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Some special caseswhat, you thought it was that
easy?
Any set of numbers such that (3a5,a)
No solution
Any set of numbers such that (-5a,a,3)
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A word problemgag!!

• A small corporation borrowed 1,500,000 to expand
  its product line. Some of the money was borrowed
  at 8, some at 9 and some at 12. How much was
  borrowed at each rate if the annual interest was
  133,000 and the amount borrowed at 8 was 4
  times the amount borrowed at 12?

800,000 at 8 500,000 at 9 200,000 at 12