Project ForgeEngineering Mathematics
Linear Algebra
GATE 2011
Medium
Let λ1=−1 and λ2=3 be the eigenvalues and V1=(1,0) and V2=(1,1) be the corresponding eigenvectors of a real 2×2 matrix R. Given that P=(V1 V2), which ONE of the following matrices represents P⁻¹RP?
- A[[0,−1],[3,0]]
- B[[0,3],[−1,0]]
- C[[3,0],[0,−1]]
- [[−1,0],[0,3]]
Explanation
By definition of eigenvalue diagonalization, when P's columns are the eigenvectors of R, P⁻¹RP is exactly the diagonal matrix of the corresponding eigenvalues, diag(λ1,λ2)=[[−1,0],[0,3]].
Source: GATE CH 2011 (2011)
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