[1 1 = 0 1 1 = Lo o 1 [1 -1 01 Compute T, in the three steps, using U and U-1 in U-1 = |0 - triu(ones(3). 1 -1 Lo 1. a. Check that T,=U*U, where U has 1's on the main diagonal and -1's along the diagonal above. Its transpose UT is lower triangular. b. Check that UU-' = I when U-ª has l's on and above the main diagonal. c. Invert UTU to find T;=(U-1)(U-)7. Inverse come in reverse order

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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[1 1
= 0 1 1 =
Lo o 1
[1 -1
01
Compute T, in the three steps, using U and U-1 in U-1 = |0
- triu(ones(3).
1
-1
Lo
1.
a. Check that T,=U*U, where U has 1's on the main diagonal and -1's along the diagonal above. Its transpose UT
is lower triangular.
b. Check that UU-' = I when U-ª has l's on and above the main diagonal.
c. Invert UTU to find T;=(U-1)(U-)7. Inverse come in reverse order
Transcribed Image Text:[1 1 = 0 1 1 = Lo o 1 [1 -1 01 Compute T, in the three steps, using U and U-1 in U-1 = |0 - triu(ones(3). 1 -1 Lo 1. a. Check that T,=U*U, where U has 1's on the main diagonal and -1's along the diagonal above. Its transpose UT is lower triangular. b. Check that UU-' = I when U-ª has l's on and above the main diagonal. c. Invert UTU to find T;=(U-1)(U-)7. Inverse come in reverse order
Expert Solution
Solution: part a

Given: U-1=1-1001-1001-1=111011001

T3=UTU =1-1001-1001T1-1001-1001=100-1100-111-1001-1001=1-10-12-10-12

 

Part b:

Checking

UU-1=1-1001-1001111011001=100010001

steps

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