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Linear transformations

General · Mathematics

Study notes

Q: Is T(x,y) = (x²,y) linear? What about R(x,y) = (-y,x)? T: T(2(1,0)) = (4,0) but 2T(1,0) = (2,0): NOT linear! R: R(u+v) = R(u)+R(v) ✓, R(cu) = cR(u) ✓: LINEAR! (R: 90° rotation!) Matrices: R = [[0,-1],[1,0]]!

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