Civil Engineering > GATE 2017 SET-2 > Mathematics
Consider the following simultaneous equations (with c1 and c2 being constants):
3x1 + 2x2= c1
4x1 + x2 = c2
The characteristic equation for these simultaneous equations is
3x1 + 2x2= c1
4x1 + x2 = c2
The characteristic equation for these simultaneous equations is
Correct : A
Consider the following simultaneous equations (with c1 and c2 being constants):
3x1 + 2x2 = c1
4x1 + x2 = c2
The characteristic equation for these simultaneous equations is?
The coefficient matrix A is:
| 3 2 |
| 4 1 |
The characteristic equation is found using det(A − λI) = 0
A − λI = | (3−λ) 2 |
| 4 (1−λ) |
det(A − λI) = (3−λ)(1−λ) − (2)(4) = 0
= 3 − 3λ − λ + λ2 − 8 = 0
= λ2 − 4λ + 3 − 8 = 0
= λ2 − 4λ − 5 = 0
The characteristic equation is λ2 − 4λ − 5 = 0 (Option A)
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