Question 2 Given the following matrix A, cos sin A sin cos 0 0 00 (a) Show that matrix A is invertible for all values of 0. (b) Using the result of (a), show that det(AT) = det(A). 1 (c) Using the result of (a), show that det (kA) = k³det(A), where k is a scalar.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 1E
icon
Related questions
Question
Question 2
Given the following matrix A,
cos
sin
A sin cos 0 0
00
(a) Show that matrix A is invertible for all values of 0.
(b) Using the result of (a), show that det(AT) = det(A).
1
(c) Using the result of (a), show that det (kA) = k³det(A), where k is a scalar.
Transcribed Image Text:Question 2 Given the following matrix A, cos sin A sin cos 0 0 00 (a) Show that matrix A is invertible for all values of 0. (b) Using the result of (a), show that det(AT) = det(A). 1 (c) Using the result of (a), show that det (kA) = k³det(A), where k is a scalar.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9780998625720
Author:
Lynn Marecek
Publisher:
OpenStax College
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax