Let f : R² → R be defined by f((x,y)) 5x + 7y. Is f a linear transformation? ((x1, Y1) + (®2, Y2)) = ((x1, Y1)) + f({x2, Y2)) = + oes f({x1,y1) + (x2, y»)) = f((x1,41)) + f({x2,y»)) for all (x1, y1), (x»,y») e R??

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let f : R?
→ R be defined by f((x, y)) = 5x + 7y. Is f a linear transformation?
a. f({x1,Yı) + (x2, Y2)) :
f({x1, Y1)) + f({x2, Y2)) =
+
Does f((x1,Y1) + (x2, Y2)) = f(x1, Y1)) + f((x2, Y2)) for all (01, Y1), (x2, Y2) E R?
Transcribed Image Text:Let f : R? → R be defined by f((x, y)) = 5x + 7y. Is f a linear transformation? a. f({x1,Yı) + (x2, Y2)) : f({x1, Y1)) + f({x2, Y2)) = + Does f((x1,Y1) + (x2, Y2)) = f(x1, Y1)) + f((x2, Y2)) for all (01, Y1), (x2, Y2) E R?
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