Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Engineering Mathematics Linear Algebra Eigenvalues
For t ∈ ℝ, define \(M(t)=\left(\begin{array}{ccc}1 & t & 0 \\ 1 & 1 & t^{2} \\ 0 & 1 & 1\end{array}\right)\)
Then which of the following statements is true?
1
det M(t) is a polynomial function of degree 3 in t
2
det M(t) = 0 for all t ∈ ℝ
3
det M(t) is zero for infinitely many t ∈ ℝ
4
det M(t) is zero for exactly two t ∈ ℝ
5
Question Not Attempted