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Question

Show that the transformation T(ax+b)=ax+2T(a x+b)=a x+2 is not linear.

Solution

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Answered 1 year ago
Answered 1 year ago

Notice that

T(2x)=2x+22x+4=2(x+2)=2T(x)\begin{align*} T(2x) = 2x+2 \neq 2x+4 = 2(x+2) = 2T(x) \end{align*}

so TT is not linear.

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