Project ForgeEngineering Mathematics
Linear Algebra
GATE 2009
Medium
The eigenvalues of matrix A=[[1,2],[4,3]] are 5 and −1. Then the eigenvalues of −2A+3I (I is a 2×2 identity matrix) are
- −7 and 5
- B7 and −5
- C−1/7 and 1/5
- D1/7 and −1/5
Explanation
If λ is an eigenvalue of A, then −2λ+3 is the corresponding eigenvalue of −2A+3I. For λ=5: −10+3=−7. For λ=−1: 2+3=5. Eigenvalues: −7 and 5.
Source: GATE CH 2009 (2009)
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