Let T: IR -IRW be a linear transformation. (a) If X is in IR, we say that

Question:

Let T: IR" -»IRW be a linear transformation.
(a) If X is in IR", we say that X is in the kernel of T if T(X) = 0. If X1 and X2 are both in the kernel of T, show that aX1 + bX2 is also in the kernel of T for all scalars a and b.
(b) If Y is in R", we say that Y is in the image of T if Y= T(X) for some X in R". If Y1, and Y2 are both in the image of T, show that aY1 + bY2 is also in the image of T for all scalars a and b.