The document discusses finding the inverse of square matrices to solve systems of linear equations. It defines an inverse matrix as a matrix that when multiplied by the original matrix results in the identity matrix. For a matrix to have an inverse, it must be nonsingular. The document presents methods for finding the inverse of 2x2 and 3x3 matrices, including using the determinant and shortcut formulas. It explains how to use the inverse of the coefficient matrix to solve systems of linear equations. Examples are provided to illustrate calculating inverses and using them to solve systems.

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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