Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Algebra Linear Dependence, Basis & Dimension
For a positive integer n, let Pn denote the vector space of polynomials in one variable x with real coefficients and with degree ≤ n. Consider the map T : P2 → P4 defined by T(p(x)) = p(x2). Then
1
T is a linear transformation and dim range (T) = 5.
2
T is a linear transformation and dim range (T) = 3.
3
T is a linear transformation and dim range (T) = 2.
4
T is not a linear transformation.
5
Question Not Attempted