MATRIX INVERSE

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MATRIX INVERSE
Pamela Leutwyler
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I
A Square matrix with 1s on the diagonal and 0s
elsewhere Is called an IDENTITY MATRIX.
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A square matrix A has an inverse if there is a
matrix A-1 such that AA-1 I
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Only one to one mappings can be inverted
?
Is the projection of onto
Is the counterclockwise Rotation of
through degrees.
?
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Only one to one mappings can be inverted
?
Is the projection of onto
Is the counterclockwise Rotation of
through degrees.
P is NOT invertible
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P is NOT 1-1.
v could be any one of many vectors
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Now we will develop an algorithm to find the
inverse for a matrix that represents an
invertible mapping.
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A-1
A
I

To solve for a, b, c, reduce
To solve for d, e, f, reduce
To solve for g, h, j, reduce
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It is more efficient to do the three problems
below in one step
To solve for a, b, c, reduce
To solve for d, e, f, reduce
To solve for g, h, j, reduce
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It is more efficient to do the three problems
below in one step
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It is more efficient to do the three problems
below in one step
1
1
0
- 1
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It is more efficient to do the three problems
below in one step
0
1
-2
3
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It is more efficient to do the three problems
below in one step
7
0
-4
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It is more efficient to do the three problems
below in one step
3
-8
4
0
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A I
reduces to
I A-1