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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Question

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
=

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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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