If the system of linear equations:x-ky-z=0,kx-y-z=0,x+y-z=0,has nonzero solutions, then possible values of k areans.
Question
If the system of linear equations:
x - ky - z = 0,
kx - y - z = 0,
x + y - z = 0,
has nonzero solutions, then possible values of k are?
Solution
The system of linear equations given is:
- x - ky - z = 0
- kx - y - z = 0
- x + y - z = 0
For a system of linear equations to have non-zero solutions, the determinant of the coefficient matrix must be equal to zero.
The coefficient matrix for the given system is:
| 1 -k -1 | | k -1 -1 | | 1 1 -1 |
The determinant of this matrix is:
1*(-1*-1 - -11) - -k(-1*-1 - -11) - -1(k*-1 - -1*1) = 1 - k - 1 = -k
Setting this equal to zero gives k = 0.
So, the possible value of k for the system to have non-zero solutions is k = 0.
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