Coles Hammond
10/19/2023 · Primary School
Discuss according to the value(s) of \( \lambda \), the nature of the solution(s) of the system represented by the augmented matix \( \left[\begin{array}{llll}1 & 0 & \lambda^{2} & \lambda \\ 1 & 0 & 1 & 1 \\ 1 & 2 & 3 & -1\end{array}\right] \) Determine the solution(s) of the corresponding system whenever possible:
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The nature of the solutions depends on the value of \( \lambda \). If \( \lambda = \pm 1 \), the system is inconsistent and has no solutions. If \( \lambda \neq \pm 1 \), the system is consistent and has a unique solution.
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