Let T : R3 → R3 be defined by the formula
T (x, y, z) =
1 −1 3
5 6 −4
7 4 2
x
y
z
Then find
(a) the kernel, ker(T ), and hence the nullity, n(T ), of T .
(b) use the Rank-Nullity Theorem to find the rank, r(T ), of T
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