Homework Sourseb Is T an onto surjective map Why or why notSolutionSince T
b.) Is T an onto (surjective) map? Why or why not?
Solution
Since T ((x,y,z)T) = (x,y)T, we have T(e1) = T ((1,0,0)T) = (1,0)T , T(e2)= T((0,1,0)T)= (0,1)T and T( e3 ) = T((0,0,1)T)= (0,0)T. Therefore, the standard matrix of T is
1
0
0
0
1
0
(b) T is a surjective map, because any element (x,y)T of R2 has several pre-images (x,y,z)T in R3 where z is arbitrary.
| 1 | 0 | 0 |
| 0 | 1 | 0 |
