Project ForgeEngineering Mathematics
Linear Algebra
GATE 2016
Hard
The number of linearly independent eigenvectors of matrix A = [[2,1,0],[0,2,0],[0,0,3]] is __________.
2
Explanation
Eigenvalues are 2, 2, 3 (upper triangular matrix). For the repeated eigenvalue λ=2, (A-2I) has rank 1, giving only 1 independent eigenvector for that eigenvalue (the matrix is defective there). The distinct eigenvalue λ=3 contributes 1 more, for a total of 2 linearly independent eigenvectors.
Source: GATE ME 2016 Set-3 (2016)
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