March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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Elements of Numerical Linear Algebra 65
Example 3.8 Consider the coefficient matrix of the system (3.2):
A =
⎡
⎣
12 −4
511−21
3 −23
⎤
⎦
.
Augment this matrix with the 3 × 3 identity matrix:
⎡
⎣
12 −4
511−21
3 −23
100
010
001
⎤
⎦
.
Let us eliminate the elements in rows 2 and 3 of the first column using a
11
=1
as the pivotal element:
⎡
⎣
12−4
01−1
0 −815
100
−510
−301
⎤
⎦
.
We can use the second row to eliminate non-diagonal elements in the second
column:
⎡
⎣
10−2
01−1
00 7
11 −20
−510
−4381
⎤
⎦
.
Finally, we can divide row 3 by 7 and use this row to eliminate coefficients
for x
3
in other rows:
⎡
⎣
100
010
001
−9/72/72/7
−78/715/71/7
−43/78/71/7
⎤
⎦
A
−1
.
Therefore, the inverse of
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