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 ]

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ISBN: 9780135851043

Author: Lay

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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

EBK LINEAR ALGEBRA AND ITS APPLICATIONS

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 - If a matrix A is 5 3 and the product AB is 5 7,...Ch. 2.1 - How many rows does B have if BC is a 3 4 matrix?Ch. 2.1 - Let A=[2531] and B=[453k]. What value(s) of k, if...Ch. 2.1 - Let A=[2346], B=[8455], and C=[5231]. Verify that...Ch. 2.1 - Let A=[111123145] and D=[200030005]. Compute AD...Ch. 2.1 - Let A=[3612]. Construct a 2 2 matrix B such that...Ch. 2.1 - Let r1,..., rp be vectors in n, and let Q be an m ...

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.