Project ForgeEngineering Mathematics
Linear Algebra
GATE 2019
Medium
In matrix equation [A]{X}={R}, [A]=[[4,8,4],[8,16,-4],[4,-4,15]], {X}={2,1,4} and {R}={32,16,64}. One of the eigenvalues of matrix [A] is
- A4
- B8
- C15
- 16
Explanation
Notice {R} = 16×{X}: (32,16,64) = 16×(2,1,4). So [A]{X}=16{X}, meaning {X} is an eigenvector of [A] with eigenvalue 16 — no need to expand the characteristic polynomial.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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