PEA 2024 PEA Q8 | ISI MSQE

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2024 PEA Q8

Let $A$ be a $3\times 3$ matrix having eigenvalues $2,7,5$ . What is the determinant of $A+2I$ ?

Reveal answer and solution

Answer

Solution

1
If $\lambda$ is an eigenvalue of $A$ , then $\lambda+2$ is an eigenvalue of $A+2I$ . Hence the eigenvalues of $A+2I$ are $4,\,9,\,7$ , and
2
$\det(A+2I)=4\cdot 9\cdot 7=252.$

Answer structure / marking notes

Determinant equals the product of eigenvalues (with multiplicity).

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2024/ISI_MSQE_PEA_2024_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.