L:Mat3×3(R)→Mat3×3(R)
If L(A)={A^−1 if det(A)≠0
0 if det(A)≠0
be defined as. Is L linear transformation?
b) L:P2→P3 ,L(at^2 +bt +c)= at^3 +(c+b)t^2
Let be a linear transformation defined as .
(i) Find a basis for the nucleus of L.
(ii) Find a basis for the image space im(L) of L.
(iii) Let the standard base of P2 be BP2 and the standard base of P3 be BP3. Find the representation matrix of L with respect to the base pair BP2,BP3.