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Lines in planes - class-XII
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$x + 2y + 3z = 0$
$2x + 3y + 4z = 0$
$7x + 13y + 19z =0$
$7x + 13y + 19z =0$
The system of equations have non trivial solutions
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A
True
💡 Explanation:
A system of homogeneous linear equations has non-trivial solutions if the determinant of the coefficient matrix is zero. The determinant of [[1, 2, 3], [2, 3, 4], [7, 13, 19]] is 1(57-52) - 2(38-28) + 3(26-21) = 5 - 20 + 15 = 0. Since the determinant is zero, non-trivial solutions exist.