GATE 2024 ST – Question 59
Matrix Theory · Eigenvalues and Matrix Decompositions · 2 marks · Numerical answer
A is real 2×2 with trace 5,determinant 6. The characteristic polynomial of (A+I)⁻¹ is x²−bx+c. Find b/c (integer).
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Show answer and explanation
Correct answer: 7 to 7
Explanation
A has eigenvalues 2,3, so (A+I)⁻¹ has eigenvalues 1/3,1/4. Hence b=7/12,c=1/12 and **b/c=7**.
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