If the Eigen value of the matrix [2 3, x -1] are -y and x-1, then x =?
- 6
- 5
- 4
- None of these
Explanation
For matrix A = [, [x, -1]] with eigenvalues λ₁ = -y and λ₂ = x-1[2][3]
Use 2 properties of eigenvalues:
1) Sum = Trace
λ₁ + λ₂ = 2 + (-1) = 1
→ -y + (x-1) = 1
→ x - y = 2 → y = x - 2
2) Product = Determinant
λ₁ × λ₂ = 2(-1) - 3(x) = -2 - 3x
→ (-y)(x-1) = -2 - 3x
Put y = x - 2:
-(x-2)(x-1) = -2 - 3x
-(x² - 3x + 2) = -2 - 3x
-x² + 3x - 2 = -2 - 3x
x² - 6x = 0
x(x - 6) = 0
x = 0 or x = 6Last verified on 04-06-2026
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