By and Bw, respectively, and a linear transformation T: V → W. Determine the matrix of
T with respect to By and Bw. Determine the rank and nullity of T.
(a) V = R³, W = R², By =
(b) V = R₂[X], W
-(0)·()·())-²- - ()-(-))-
Bw
=
3
defined by
(c) V = W = M2x2 (R), By
fined by
-0-0)
T
=
= R¹, By = (1, X, X², X³), Bw
N
=
T(a+bX+cX²) =
2a
a
T (05) - (²
Т
C d
-(0000)--
=
b+c
a
b
C
(a+b+c)
Bw
- (( ) ( ) ( ) ( . )). T I. de
=
is
T is defined by
b+c
6+)
2d
Fig: 1