- #1
hachi_roku
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Homework Statement
let T: R^4 --->R^3, where T(v)=A(v) and matrix A is defined by
A = [2 1 -1 1
1 2 0 5
4 -1 1 0
Find kernel of T, nullity of T, range of T and rank of T
Homework Equations
The Attempt at a Solution
ok. ker(T) = Null(A)
[2 1 -1 1][v1]= [0]
[1 2 0 5] [v2]= [0]
[4 -1 1 0][v3] = [0]
[v4]
simplifying using gauss jordan:
1 0 0 1/6 [v1] [0]
0 1 0 29/12 [v2] = [0]
0 0 1 7/4 [v3] [0]
[v4]
v1 + 1/6V4 = 0
V2 + 29/12v4 = 0
v3 + 7/4v4 = 0 so [ -1/6v4]
[-29/12v4] V all real
[-7/4v4]
[v4]
range and rank i got 3
is this right?