Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Vector Spaces
Let V be the vector space of all real polynomials of degree ≤ 10. Let Tp(x) = p'(x) for p ∈ V be a linear transformation from V to V. Consider the basis {1, x, x2,…,x10} of V. Let A be the matrix of T with respect to this basis. Then
1
Trace A = 1
2
det A = 0
3
there is no m ∈ ℕ such that Am = 0
4
A has a non zero eigenvalue