Use partitioned matrices to prove by induction that the

Chapter 2, Problem 23E

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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.]

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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

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