A function f(x) on Rn is called homogeneous of degree k if f(cx) = ci(x) for all scalars c. (a) If a Rn is

A function f(x) on Rn is called homogeneous of degree k if f(cx) = ci(x) for all scalars c.
(a) If a ˆˆ Rn is a fixed vector, show that a linear form £(x) = a . x = a1X1 +-----+ anxn is homogeneous of degree 1.
(b) Show that a quadratic form

is homogeneous of degree 2.
(c) Find a homogeneous function of degree 2 on R2 that is not a quadratic form.

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