Statement 1: If the system of equations x + k y + 3 z = 0 , 3 x + k y − 2 z = 0 , 2 x + 3 y − 4 z = 0 has a nontrivial solution, then the value of k is 2 31 . Statement 2: A system of three homogene

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Statement 1: If the system of equations x + k y + 3 z = 0 , 3 x + k y − 2 z = 0 , 2 x + 3 y − 4 z = 0 has a nontrivial solution, then the value of k is 2 31 ​ . Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.

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Given system of equations is ​ x + k y + 3 z = 0 3 x + k y − 2 z = 0 2 x + 3 y − 4 z = 0 ​ Since, system has non-trivial solution ⇒ ⇒ ​ ∴ ​ 1 3 2 ​ k k 3 ​ 3 − 2 − 4 ​ ​ = 0 1 ( − 4 k + 6 ) − k ( − 12 + 4 ) + 3 ( 9 − 2 k ) = 0 4 k + 33 − 6 k = 0 ⇒ k = 2 33 ​ ​ Hence, statement - 1 is false. Statement- 2 is the property. It is a true statement.

Mathematics - Determinant Question with Solution | TestHub

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