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Linear Algebra With Applications
Found in: Page 54
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Consider the transformation T from R2 to role="math" localid="1659714471562" R2that rotates any vector x through a given angle θ in the counterclockwise direction. Compare this with Exercise 33. You are told that T is linear. Find the matrix of T in terms of θ.

Matrix for T will be cosθ-sinθsinθcosθ

See the step by step solution

Step by Step Solution

Step by step Explanation: Step1: Linear Transformation

A transformation from RmRn is said to be linear if the following condition holds:

  1. Identity of Rm should be mapped to identity of Rn.
  2. T(a+b)=T(a)+T(b)For all a,bRm.
  3. T(ca)=cT(a) Where c is any scalar and aRm.

Step2: Transformation

Given T is linear transformation fromR2R2.

Let be any point ofR2.

Then we can write the transformation.


Hence, the matrix for T will be [cosθ-sinθsinθcosθ].

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