Teaching CSIR NET Mock Test Series Engineering Mathematics Linear Algebra Matrix Algebra

Let T : ℝ3 → ℝ3 be the linear transformation defined by T(x, y, z) = (x + y, y + z, z + x) for all (x, y, z) ∈ ℝ3. Then

1
rank (T) = 0, nullity (T) = 3
2
rank (T) = 2, nullity (T) = 1 
3
rank (T) = 1, nullity (T) = 2
4
rank (T) = 3, nullity (T) = 0
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