Finding the inverse of a matrix.

1. March 09, 2012
8.3 The Inverse of a
Square Matrix
Objective: Find and use the inverse
matrix to solve systems of linear
equations.
Standard: Linear Algebra 9.0
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2. March 09, 2012
What's a MULTIPLICATIVE
INVERSE??
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3. March 09, 2012
To be an inverse matrix:
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4. March 09, 2012
Ex. 1﴿ Show that B is the Inverse of A.
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5. March 09, 2012
Do all matrices have an inverse?
Singular:
Nonsingular ﴾aka: ________﴿
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6. March 09, 2012
Ex. 2﴿ Find the inverse of A if it exists.
A=
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7. March 09, 2012
The "Shortcut" for a 2x2 matrix
If… and…
ad – bc ≠ 0
then…
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8. March 09, 2012
Ex. 2 Revisited﴿ Find the inverse of A if
it exists.
A=
Ex. 3﴿ Find the inverse of A if it exists.
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9. March 09, 2012
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10. March 09, 2012
Inverse of a 3x3 Matrix
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11. March 09, 2012
Using Inverses for Systems
of Equations
The coefficient matrix…
`
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12. March 09, 2012
Ex. 4﴿ Solve the systems using matrices.
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13. March 09, 2012
Ex. 5﴿ Solve the system using matrices.
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14. March 09, 2012
Assignment:
8.3 p. 608 #4, 5, 11, 15, 17, 25,
27, 46, 49
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