Page 123 - DMTH502_LINEAR_ALGEBRA
P. 123
Unit 7: Algebra of Linear Transformation
Answers: Self Assessment Notes
1. (i) I identity transformation
(ii) (MD) 2
2. (i) DJ p(x) = I p(x)
(ii) no JD DJ
3. (ii), (iv) are linear transformations.
4. (i) (U + T) (x , x ) = (x + x , x )
1 2 1 2 1
(ii) (U + T) (x , x ) = (x , 0)
1 2 2
(iii) (TU) (x , x ) = (0, x )
1 2 1
5. Yes T is invertible as , , are standard basis of C space.
3
1 2 3
7.7 Further Readings
Books Kenneth Hoffman and Ray Kunze, Linear Algebra
I.N. Herstein, Topics in Algebra
Michael Artin, Algebra.
LOVELY PROFESSIONAL UNIVERSITY 117
