List of top Mathematics Questions on Applications of Determinants and Matrices asked in MET

The system of linear equations \[ x+y+z=0,\; 2x+y-z=0,\; 3x+2y=0 \] has

The value of \( a \) for which the system \[ ax + y + z = 0,\; x + ay + z = 0,\; x + y + z = 0 \] has non-zero solutions is

Sum of the series to \(n\) terms \(5 + 7 + 13 + 31 + 85 + \ldots\) is
Which of the following statements is/are correct?
I. Adjoint of a unit matrix is a unit matrix.
II. \( A (\text{adj } A) = (\text{adj } A) A = |A|I \)
III. Adjoint of a symmetric matrix is symmetric.
IV. Adjoint of a diagonal matrix is a diagonal matrix.