Project ForgeEngineering Mathematics
Linear Algebra
GATE 2010
Medium
One of the eigen vectors of the matrix A = [[2,2],[1,3]] is
- {2,-1}
- B{2,1}
- C{4,1}
- D{1,-1}
Explanation
Characteristic equation: (2-λ)(3-λ)-2=0 ⟹ λ²-5λ+4=0 ⟹ λ=1,4. For λ=1: (A-I)v=0 gives [[1,2],[1,2]]v=0 ⟹ x1+2x2=0, satisfied by v=(2,-1).
Source: GATE ME 2010 (2010)
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