Whether the function is a linear transformation or not. T : R^{2} rightarrow R^{2}, T(x,y)=(x,y^{2})

allhvasstH 2021-01-08 Answered
Whether the function is a linear transformation or not.
T : R2R2,T(x,y)=(x,y2)
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Expert Answer

okomgcae
Answered 2021-01-09 Author has 93 answers
Calculation:
The function is defined as,
T(x,y)=(x,y2)
Assume two general vectors u=(u1,u2) and v=(v1,v2)
Then u+v=(u1+v1,u2+v2)
cu=(cu1,cu2)
The function is a linear transformation if it satisfies the two properties as mentioned in the approach part.
Compute T(u+v) and T(u)+T(v) as
T(u+v)=T(u1+v1, u2+v2)
=(u1+v1, (u2+v2)2)
=(u1+v1, u22+v22 + 2u2v2)
T(u)+T(v)=T(u1, u2)+T(v1 ,v2)
=(u1, u22)+(v1, v22)
=(u1+v1, u22+v22)
Since T(u+v)qT(u)+T(v), the first property is not satisfied.
Therefore, the function is not a linear transformation.
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