GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/14

Question 14 (Textile Technology & Fibre Science)

The determinant of a 3 × 3 matrix 𝐴 is 30. If 2 and 3 are two Eigenvalues of 𝐴, then the third Eigenvalue of 𝐴 (in integer) is _.

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Given in the question-

Determinant of matrix A (3×3)=30

Let third eigen value of A=A3

Eigen values of A are=2,3, A3

\left | A \right |=30

2 x 3 x A3=30

6 x A3=30

A3=5 (Ans)

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