Project ForgeEngineering Mathematics
Linear Algebra
GATE 2008
Medium
The eigenvectors of the matrix [[1,2],[0,2]] are written in the form [1,a] and [1,b]. What is a+b?
- A0
- 1/2
- C1
- D2
Explanation
For λ=1: (A-I)v=0 gives [[0,2],[0,1]]v=0 ⟹ v2=0, so eigenvector (1,0), a=0. For λ=2: (A-2I)v=0 gives -v1+2v2=0 ⟹ v1=2v2; normalizing to first component 1 gives (1, 1/2), b=1/2. a+b=0+1/2=1/2.
Source: GATE ME 2008 (2008)
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