Let V=?2×2 be the vector space of 2×2 matrices and let L:V?V be defined by L(X)=[15351]X. Hint: The image of a spanning set is a spanning set for the image.
a. Find L([?54?4?4])= [ ]
b. Find a basis for ker(L): { [ ] , [ ] }
c. Find a basis for ran(L): { [ ] , [ ] }