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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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