Is the transformation R_{\frac{\pi}{3}}(x) is linear transformation? Justify your answer.

Alexander Day

Alexander Day

Answered question

2022-02-13

Is the transformation Rπ3(x) is linear transformation? Justify your answer.

Answer & Explanation

ithangesf4

ithangesf4

Beginner2022-02-14Added 16 answers

Step 1
A linear transformation (or a linear map) is a function T:RnRm that satisfies the following properties:
1) T(x+y)=T(x)+T(y)
2) T(ax)=aT(x)
for any vectors x, yRn and any scalar aR
Now, since we have
Rθ=[cosθsinθ0sinθcosθ0001]
then
Rθ(x)=[cosπ3sinπ30sinπ3cosπ30001]=[1232032120001]
Now, since every matrix is a linear transformation. Hence the given transformation is a linear transformtion.

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