Engineering Analysis ENG 3420 Fall 2009
Dan C. Marinescu
Office: HEC 439 B
Office hours: Tu-Th
11:00-12:00

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2
Lecture 19
Lecture 19
Last time:
•
Midterm: solutions and discussions Today:
Today
The inverse of a matrix
Iterative methods for solving sytems of linear equations
Gauss-Siedel
Jacobi
Next Time
Relaxation
Non-linear systems

The inverse of a square
If [
A
] is a square matrix, there is another matrix [
A
]
-1
,
called the inverse of [
A
], for which [
A
][
A
]
-1
=[
A
]
-1
[
A
]=[I]
The inverse can be computed in a column by column
fashion by generating solutions with unit vectors as the
right-hand-side constants:
A
[ ]
x
1
{ }
=
1
0
0
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
A
[ ]
x
2
{
}
=
0
1
0
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
A
[ ]
x
3
{
}
=
0
0
1
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
A
[ ]
−
1
=
x
1
x
2
x
3
[
]

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Canonical base of an n-dimensional vector space
100……000
010……000
001……000
…………….
000…….100
000…….010
000…….001