Linear algebra: please solve q30 correctly and handwritten 30. Suppose that A and B are orthogonal (n xn) matri-ces. Show that AB is an orthogonal matrix.31. Let x be a nonzero vector in R², x = [a, b]¹. Finda vector y in R² such that xy = 0 and y¹y = 1.32. Let A be a real (2 x 2) matrix with only real eigen-values. Suppose that Au = λu, where u¹ u = 1.By Exercise 31, there is a vector v in R² such that

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Answered: 30. Suppose that A and B are orthogonal…

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30. Suppose that A and B are orthogonal (n xn) matri- ces. Show that AB is an orthogonal matrix.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section: Chapter Questions

Problem 17RQ

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Question

Linear algebra: please solve q30 correctly and handwritten

30. Suppose that A and B are orthogonal (n xn) matri-
ces. Show that AB is an orthogonal matrix.
31. Let x be a nonzero vector in R², x = [a, b]¹. Find
a vector y in R² such that xy = 0 and y¹y = 1.
32. Let A be a real (2 x 2) matrix with only real eigen-
values. Suppose that Au = λu, where u¹ u = 1.
By Exercise 31, there is a vector v in R² such that

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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