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MathematicsMatricesAdjointHard2 minQB

MathematicsHardsingle choice

Let $A = [a_{ij}]_{3 \times 3}$ be positive diagonal. If $adj A$ has characteristic equation $λ^{3} - 12 λ^{2} + kλ - 64 = 0$ , which is correct?

Answer:

Solution:

The positive eigenvalues of $adj A$ have sum 12 and product 64, so all three are 4. Thus $A = 2 I_{3}$ , and option C follows.

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Adjoint

⏱ 2mℹ️ Source: QB

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