Is this a linear equation y=0?

May 24, 2015

Yes it is,

by definition, a (real) linear equation is

$y = P \left(x\right) : P \left(\alpha {x}_{1} + \beta {x}_{2}\right) = \alpha P \left({x}_{1}\right) + \beta P \left({x}_{2}\right) , \forall \alpha , \beta \in \mathbb{R}$

Here you have $y = 0 , s o P \left(x\right) = 0$

Notice that

$P \left(\alpha {x}_{1} + \beta {x}_{2}\right) = 0$
$\alpha P \left({x}_{1}\right) + \beta P \left({x}_{2}\right) = \alpha \cdot 0 + \beta \cdot 0 = 0$

So it's linear.