Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Analysis Matrix Representation of Linear Transformations
Let π βΆ β4 β β4 be a linear transformation and the null space of π be the subspace of β4 given by
{(π₯1, π₯2, π₯3, π₯4) β β4 βΆ 4π₯1 + 3π₯2 + 2π₯3 + π₯4 = 0}.
If π πππ(π − 3πΌ) = 3, where πΌ is the identity map on β4 , then the minimal polynomial of π isΒ
1
π₯(π₯ − 3)Β
2
π₯(π₯ − 3)3
3
π₯3 (π₯ − 3)Β
4
π₯2 (π₯ − 3)2
5
Question Not Attempted