Consider three linear transformations : R : IR2->IR2, rotation by pi/2 cometer-clockwise S : IR2- IR", S(x, y) =(y,0,x) P : IR3-IR3, projection onto the line parallel (1,2,3) Set T = PoSoR How do I find R

To find the matrix \( R \) that represents the linear transformation **rotation by \( \pi/2 \) counter-clockwise** in \(\mathbb{R}^2\), we can use the standard approach for rotation matrices. 

### **Step 1: General form of a 2D rotation matrix**
The standard rotation matrix \( R(\theta) \) for an angle \( \theta \) in \(\mathbb{R}^2\) is:
\[
R(\theta) = 
\begin

Consider three linear transformations : R : IR2->IR2, rotation by pi/2 counter-clockwise S : IR2-> IR2, S(x, y) = (y,0,x) P : IR3->IR3, projection onto the line parallel (1,2,3) Set T = PoSoR How do I find R

Learn how to find the matrix representing the linear transformation of rotation by pi/2 counter-clockwise in R2. The solution explains the process of deriving the standard 2D rotation matrix using key concepts in linear algebra, including matrix multiplication and rotation transformations.

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Step 1: General form of a 2D rotation matrix

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