Project ForgeEngineering Mathematics
Linear Algebra
GATE 2022
Easy
If the sum and product of eigenvalues of a 2×2 real matrix [[3, p],[p, q]] are 4 and −1, respectively, then |p| is ______ (in integer).
2
Explanation
Sum of eigenvalues = trace = 3+q = 4, so q=1. Product of eigenvalues = determinant = 3q−p² = 3(1)−p² = −1, so p²=4, giving |p|=2.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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