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
Matrix A = [ 2 3 ] [ x -1 ]
Eigenvalues = -y , x-1
Rule 1: Trace = sum of eigenvalues
2 + (-1) = -y + (x-1)
1 = x - y - 1
x - y = 2 --> y = x - 2 ...eq1
Rule 2: Determinant = product of eigenvalues
2*(-1) - 3*x = (-y)*(x-1)
-2 - 3x = -y(x-1) ...eq2
Put eq1 in eq2:
-2 - 3x = -(x-2)(x-1)
-2 - 3x = -(x^2 - 3x + 2)
-2 - 3x = -x^2 + 3x - 2
x^2 - 6x = 0
x(x - 6) = 0
x = 0 or x = 6
Last verified on 04-06-2026
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- [1 2, 2 1, 1 3] [x1, x2, x3] = [9 7]
- [3 1, 2 1, 1 2] [x1, x2, x3] = [9 7]
- [1 2, 2 1, 1 3] [x1, x2, x3] = [7 9]
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- d²x/dt² = - m²x
- d²x/dt² = + m²x
- d²x/dt² = ± m²x
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- 6
- 5
- 4
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- 2
- -2
- -1
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
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