To determine Find the inverse of the rotation matrix R . Explanation Given information: The given matrix R is [ 0.8 0.0 − 0.6 0.0 1.0 0.0 0.6 0.0 0.8 ] . Calculation: Write the given matrix with identity matrix. R = [ 0.8 0.0 − 0.6 0.0 1.0 0.0 0.6 0.0 0.8 | 1 0 0 0 1 0 0 0 1 ] (1) The vertical line in Equation (1) denotes the separation of two matrices. The first element a 11 in the Equation (1) should be 1. Replace the row 1 by dividing with 0.8 with each element. R = [ 0.8 0.0 − 0.6 0.0 1.0 0.0 0.6 0.0 0.8 | 1 0 0 0 1 0 0 0 1 ] → R 1 0.8 = [ 0.8 0.8 0.0 0.8 − 0.6 0.8 0.0 1.0 0.0 0.6 0.0 0.8 | 1 0.8 0 0.8 0 0.8 0 1 0 0 0 1 ] = [ 1 0.0 − 0.75 0.0 1.0 0.0 0.6 0.0 0.8 | 1.25 0 0 0 1 0 0 0 1 ] (2) The elements a 21 and a 31 in Equation (1) should be 0. The element a 21 is already zero. Replace the elements of row 3 by subtracting 0.6 times the element of row 1 from the corresponding element in row 3. R = [ 1 0.0 − 0.75 0.0 1.0 0.0 0.6 0.0 0.8 | 1.25 0 0 0 1 0 0 0 1 ] → R 3 − 0.6 R 1 = [ 1 0.0 − 0.75 0.0 1.0 0.0 { 0.6 − 0.6 ( 1 ) } { 0.0 − 0.6 ( 0 ) } { 0.8 − 0.6 × − 0.75 } | 1.25 0 0 0 1 0 { 0 − 0.6 × 1.25 } { 0 − 0.6 × 0 } { 1 − 0.6 × 0 } ] = [ 1 0.0 − 0.75 0.0 1.0 0.0 0.0 0.0 1.25 | 1.25 0 0 0 1 0 − 0.75 0 1 ] (3) The bottom row element a 22 in Equation (3) should be 1

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 16.3, Problem 42E

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Chapter 16.3, Problem 41E

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Chapter 16 Solutions

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

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