Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Engineering Mathematics Linear Algebra Matrix Algebra
Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S). then which one of the following is TRUE?
1
nullity of T = nullity of S
2
dimension of U ≠ dimension of W
3
If dimension of V = 3, dimension of U = 4, then P is not identically zero
4
If dimension of V= 4, dimension of U = 3, and T is one-one, then P is identically zero
5
Question Not Attempted