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      Question

      If the homogeneous system of equations x + y + z

      = 0 2x + 3y + 4z = 0 has a non-trivial solution, then the value of k is: 3x + 5y + kz = 0
      A 6 Correct Answer Incorrect Answer
      B 9 Correct Answer Incorrect Answer
      C 7 Correct Answer Incorrect Answer
      D 8 Correct Answer Incorrect Answer

      Solution

      We are given a homogeneous system of equations: x + y + z = 0 2x + 3y + 4z = 0 3x + 5y + kz = 0 We are told the system has a non-trivial solution , and we are to find the value of A homogeneous system has a non-trivial solution if and only if the determinant of the coefficient matrix is zero , i.e., the rows are linearly dependent . Write the coefficient matrix

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