Answered: An upper triangular matrix A is one…

An upper triangular matrix A is one whose entries a^ij are zero if i > j. Prove that the product C = AB of two upper triangular matrices is upper triangular.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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Question

An upper triangular matrix A is one whose entries a^ij are zero if i > j.
Prove that the product C = AB of two upper triangular matrices is upper triangular.
Hint: based on the interpretation of matrix multiplication AB as forming linear combinations of the columns of A

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