Algebra

The number of values of k for which the linear equations4x + ky + 2z = 0kx + 4y + z = 02x + 2y + z = 0possess a non-zero solution is

nikhil

12 Years agoGrade

1 Answer

Latika Leekha

12 Years ago

The given system is

4x + ky + 2z = 0

kx + 4y + z = 0

2x + 2y + z = 0

For a non-zero solution, the determinant of the system must be zero.

Hence, 4(4-2) – k(k-2) + 2(2k-8) = 0

This yields (16 – 8 – k² + 2k + 4k -16) = 0.

Hence, -k² + 6k – 8 = 0

This gives k = 4, 2.

Hence, the given system has a non-zero solution for two values of k.

Thanks & Regards

Latika Leekha

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The number of values of k for which the linear equations4x + ky + 2z = 0kx + 4y + z = 02x + 2y + z = 0possess a non-zero solution is

nikhil

1 Answer

Latika Leekha

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