Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Algebra of Linear Transformations
Statement P: Consider the linear transformation \( T : \mathbb{R^4} → \mathbb{R^4} \) given by: \(T(x, y, z, u) =( 3x, 2y, 0, 0 ) ∀ (x, y, z , u) ∈ \mathbb{R^4} \) then Rank of T > Nullity of T.
Statement Q: Let \( T : \mathbb{R^3} → \mathbb{R^3} \) be defined by \(T(x, y, z,) =( 3x, 2y, 0 ) ∀ (x, y, z ) ∈ \mathbb{R^3} \) and \( S : \mathbb{R^2} → \mathbb{R^2} \) be defined by S(x, y)= (2x, 3y) be linear transformation on the real vector spaces \( \mathbb{R^3} \) and \( \mathbb{R^2} \), respectively. Then T and S both are singular.
1
Both P and Q are True
2
Neither P nor Q True
3
Q is correct but P is false
4
P is True but Q is false