List of top Mathematics Questions on Determinants asked in CBSE CLASS XII

Obtain the value of \[ \Delta= \begin{vmatrix} 1+x & 1 & 1\\ 1 & 1+y & 1\\ 1 & 1 & 1+z \end{vmatrix} \] in terms of \(x\), \(y\) and \(z\).

Further, if \[ \Delta=0 \] and \(x\), \(y\) and \(z\) are non-zero real numbers, prove that \[ \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=-1. \]

If $\begin{vmatrix} 0 & 4 & 2a \\ -2 & a & -1 \\ -1 & -2 & 5 \end{vmatrix} = -86$, then the sum of all possible values of $a$ is:

Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

If \[ \begin{vmatrix} -1 & -2 & 5 \\ -2 & a & 4 \\ 0 & 4 & 2a \end{vmatrix} = -86 \] then the sum of all possible values of \( a \) is