Page 166 - 35Linear Algebra

166 Matrices

This can be checked explicitly simply by block-multiplying these three ma-
trices.

Block LDU Explanation

Example 100 For a 2 × 2 matrix, we can regard each entry as a 1 × 1 block.

1 2 1 0 1 0 1 2
=
3 4 3 1 0 −2 0 1
By multiplying the diagonal matrix by the upper triangular matrix, we get the standard
LU decomposition of the matrix.

You are now ready to attempt the first sample midterm.

7.8 Review Problems

Reading Problems 7 ,8
Webwork:
LU Decomposition 14

1. Consider the linear system:

x 1 = v 1

2 1
l x +x 2 = v 2
1
. . . . . .
n 1
n
n 2
l x +l x + · · · + x = v n
2
1
1
(i) Find x .
2
(ii) Find x .
3
(iii) Find x .
166