Let L: R4 †’ R3 be defined by
L([u1 u2 u3 u4]) = [u1 u2+u3 u3+ u4]
Let S and T be the natural bases for R4 and R3, respectively. Let

And

(a) Find the representation of L with respect to S and T.
(b) Find the representation of L with respect to S' and T'
(c) Find L ([2 1 -1 3]) by using the matrices obtained in parts (a) and (b) and compare this answer with that obtained from the definition for L.

Transcribed Image Text:

S'={[1 0 0 1],[0 [ 1 0 0], [o 0 1]. o]] 0 I00I 00