Is this a correct way to prove T is not a linear transformation? – math.stackexchange.com

Is this a correct way to prove T is not a linear transformation? – math.stackexchange.com

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I have the following transformation $T:\mathbb{R}^2 \longrightarrow \mathbb{R}^3$ defined by $T\left( x, y \right) = \left( y, x, x^2 + y^2 \right).$ I know the transformation is not linear but would ...

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