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Use partitioned matrices to prove by induction that the
Chapter 2, Problem 23E(choose chapter or problem)
Problem 23E
Use partitioned matrices to prove by induction that the product of two lower triangular matrices is also lower triangular. [Hint: A(k + 1) × (k + 1) matrix A1 can be written in the form below, where a is a scalar, v is in ℝk , and A is a k × k lower triangular matrix. See the Study Guide for help with induction.]
Questions & Answers
QUESTION:
Problem 23E
Use partitioned matrices to prove by induction that the product of two lower triangular matrices is also lower triangular. [Hint: A(k + 1) × (k + 1) matrix A1 can be written in the form below, where a is a scalar, v is in ℝk , and A is a k × k lower triangular matrix. See the Study Guide for help with induction.]
ANSWER:
Solution:-
Step1
Given that
A(k + 1) × (k + 1) matrix A1 can be written in the form below, where a is a scalar, v is in ℝk , and A is a k × k lower triangular matrix.
Step2
To find
Prove by induction that the product of two lower triangular matrices is also lower triangular.
Step3