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for what values of k, if any, is the transformation T(x,y) = 3y + k linear?

for what values of k, if any, is the transformation T(x,y) = 3y + k linear?

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Answer #1

A linear transformation between two vector spaces and is a map such that the following hold:

1. for any vectors and in , and

2. for any scalar .

So, applying the first condition on the given function T, we have

But, we have

From equations (1) and (2), we have

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