Explanation Given information: From Exercise 7. The transformation matrix is [ 1 / 2 − 3 / 2 3 + 4 3 3 / 2 1 / 2 4 − 3 3 0 0 1 ] . Calculation: The transformation matrix is [ 1 / 2 − 3 / 2 3 + 4 3 3 / 2 1 / 2 4 − 3 3 0 0 1 ] . The above 3 × 3 matrix is of the form [ A p 0 T 1 ] with A is a 2 × 2 matrix and p is in R 2 . The matrix A is [ 1 / 2 − 3 / 2 3 / 2 1 / 2 ] . The matrix p is [ 3 + 4 3 4 − 3 3 ]

Linear Algebra and Its Applications (5th Edition)

5th Edition

ISBN: 9780321982384

Author: David C. Lay, Steven R. Lay, Judi J. McDonald

Publisher: PEARSON

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Question

Chapter 2.7, Problem 14E

To determine

To show:

The transformation matrix [1/2−3/23+433/21/24−33001] is equivalent to a rotation about the origin followed by a translation by p.

To find: The vector p.

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Chapter 2.7, Problem 13E

Chapter 2.7, Problem 15E

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Chapter 2 Solutions

Linear Algebra and Its Applications (5th Edition)

Ch. 2.1 - Since vectors in n may be regarded as n 1...Ch. 2.1 - Let A be a 4 4 matrix and let x be a vector in 4....Ch. 2.1 - Suppose A is an m n matrix, all of whose rows are...Ch. 2.1 - In Exercises 1 and 2, compute each matrix sum or...Ch. 2.1 - In Exercises 1 and 2, compute each matrix sum or...Ch. 2.1 - In the rest of this exercise set and in those to...Ch. 2.1 - Compute A 5I3 and (5I3)A, when A=[913876418].Ch. 2.1 - In Exercises 5 and 6, compute die product AB in...Ch. 2.1 - In Exercises 5 and 6, compute die product AB in...Ch. 2.1 - If a matrix A is 5 3 and the product AB is 5 7,...

Knowledge Booster

The transformation matrix [ 1 / 2 − 3 / 2 3 + 4 3 3 / 2 1 / 2 4 − 3 3 0 0 1 ] is equivalent to a rotation about the origin followed by a translation by p. To find: The vector p.

Solution Summary: The author explains that the transformation matrix left is equivalent to a rotation about the origin followed by translation by p.

To show:

The transformation matrix [1/2−3/23+433/21/24−33001] is equivalent to a rotation about the origin followed by a translation by p.

To find: The vector p.

Want to see the full answer?

Chapter 2 Solutions

The transformation matrix [ 1 / 2 − 3 / 2 3 + 4 3 3 / 2 1 / 2 4 − 3 3 0 0 1 ] is equivalent to a rotation about the origin followed by a translation by p. To find: The vector p.

Solution Summary: The author explains that the transformation matrix left is equivalent to a rotation about the origin followed by translation by p.

To show: The transformation matrix [1/2−3/23+433/21/24−33001] is equivalent to a rotation about the origin followed by a translation by p. To find: The vector p.

Want to see the full answer?

Chapter 2 Solutions

To show:

The transformation matrix [1/2−3/23+433/21/24−33001] is equivalent to a rotation about the origin followed by a translation by p.

To find: The vector p.