A square matrix U = [ui] is said to be upper triangular whenever Wij = 0 for i>j-i.e., all entries below the main diagonal are 0. (a) If A and B are two n x n upper-triangular matrices, explain why the product AB must also be upper triangular.
A square matrix U = [ui] is said to be upper triangular whenever Wij = 0 for i>j-i.e., all entries below the main diagonal are 0. (a) If A and B are two n x n upper-triangular matrices, explain why the product AB must also be upper triangular.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please provide a proper ***proof*** to (a) and (c)
![[ui] is said to be upper triangular whenever
Wij = 0 for i> j―i.e., all entries below the main diagonal are 0.
(a)
If A and B are two n x n upper-triangular matrices, explain
why the product AB must also be upper triangular.
(b)
If Anxn and Bnxn are upper triangular, what are the diagonal
entries of AB?
(c)
L is lower triangular when lij = 0 for i<j. Is it true that
the product of two nx n lower-triangular matrices is again
lower triangular?
3.5.8. A square matrix U
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98b6e310-08ba-4e1d-a9bc-704b45d2ce6c%2F52fb6378-6be0-47d3-8d98-d247a1b0f7d2%2F5cqayw_processed.png&w=3840&q=75)
Transcribed Image Text:[ui] is said to be upper triangular whenever
Wij = 0 for i> j―i.e., all entries below the main diagonal are 0.
(a)
If A and B are two n x n upper-triangular matrices, explain
why the product AB must also be upper triangular.
(b)
If Anxn and Bnxn are upper triangular, what are the diagonal
entries of AB?
(c)
L is lower triangular when lij = 0 for i<j. Is it true that
the product of two nx n lower-triangular matrices is again
lower triangular?
3.5.8. A square matrix U
=
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Thank you, but for (b), they're asking for the diagonal of AB, not what is under the diagonal of AB. I wrote a11b11 + a22b22 + ... + annbnn
Please let me know if that's correct.
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