Determination of linear transformation

[lldk]

For this question, I have computed that a=-x/2, b=xy/4, c=-y/2. But I stuck in how to use the property(T(u+v)=T(u)+T(v)) to prove it is a linear transformation or not.

 

[Deleted member 4993]

For this question, I have computed that a=-x/2, b=xy/4, c=-y/2. But I stuck in how to use the property(T(u+v)=T(u)+T(v)) to prove it is a linear transformation or not.

Can you please show us your work for calculating a, b & c?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

For this question, I have computed that a=-x/2, b=xy/4, c=-y/2. But I stuck in how to use the property (T(u+v)=T(u)+T(v)) to prove it is a linear transformation or not.

I agree with your a, b, and c; so you've found that T((x, y)^T) = (-x/2, xy/4, -y/2)^T.

Now if u = (x₁, y₁)^T and v = (x₂, y₂)^T, what are T(u + v) and T(u) + T(v)?