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## Homework Statement

Let V be a 3 dim vector space over F and e_1 e_2 and e_3 be those fix basis

The question provide us with the linear transformation T[itex]\in[/itex]

*L*(V) such that

T(e_1) = e_1 + e_2 - e_3

T(e_2) = e_2 - 3e_3

T(e_3) = -e_1 -3e_2 -2e_3

we are ask to find the matrix of T and the basis of ker(T) and Im(T)

**2. The attempt at a solution**

I think I find the matrix right

where the matrix of T should be

1 0 -1

1 1 -3

-1 -3 -2

but the problem is I am not sure how can i find the ker(T) and Im(T)