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I am studying for a final I have tomorrow in linear algebra, and I am still having trouble understanding linear functionals. Can someone help me out with this example problem, walk me through it so I can understand exactly what a linear functional is?
Is the following a linear functional?
[tex]\ y (x)=\int_0^1\ t^2 x(t) \, dx [/tex]
[tex]\ y (x)=x(-2)+\int_0^1\ x(t^2)\, dt [/tex]
Is the following a linear functional?
[tex]\ y (x)=\int_0^1\ t^2 x(t) \, dx [/tex]
[tex]\ y (x)=x(-2)+\int_0^1\ x(t^2)\, dt [/tex]