Show that a linear transformantion T maps this segment into

Show that a linear transformantion T maps this segment into the segment between 0 and T(u).

Solution

Lets assume that x= tu for some value of t between 0 <=t <=1.

We know T is a linear transformation, so , T(tu) = t*T(u)

which is a given point on the line segment between 0 and T(u).

hence proved