Let C(λ)=(12λ0λ3λ14),C(\lambda)=\begin{pmatrix}1 & 2 & \lambda \\ 0 & \lambda & 3 \\ \lambda & 1 & 4\end{pmatrix},…

Mathematics

Problem

Let C(λ)=(12λ0λ3λ14),C(\lambda)=\begin{pmatrix}1 & 2 & \lambda \\ 0 & \lambda & 3 \\ \lambda & 1 & 4\end{pmatrix}, where λ∈R\lambda\in\mathbb R. a. (i) Evaluate det⁡(C(λ))\det\bigl(C(\lambda)\bigr) as an explicit expression in λ\lambda. b. (ii) Hence determine all real values of λ\lambda for which C(λ)C(\lambda) is invertible.

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