List of top Engineering Mathematics Questions on Matrices and Determinants asked in GATE AG

If the matrix \[ \begin{pmatrix} x & -3 \\ 2 & x - 5 \end{pmatrix} \] is singular, sum of the values of \( x \) is:

A vector \(\vec{F} = 5\hat{i} - 10\hat{j} + 8\hat{k}\) is passing through the origin of a 3-D frame. Considering the tendency of rotation in the counter clockwise direction as positive, the moment about a point \(A: (3, 4, 8)\) is:

If \(A = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}, \; B = \begin{bmatrix} a & 1 \\ b & -1 \end{bmatrix}\) and \((A + B)^2 = A^2 + B^2\), then the values of \(a\) and \(b\) are:

If \(A\) and \(B\) are square matrices of order \(3\) such that \(|A|=-1\) and \(|B|=3\), then \(|3AB|\) equals:

The matrix \[ \begin{bmatrix} 3 - x & 2 & 2 \\ 2 & 4 - x & 1 \\ -2 & -4 & -1 - x \end{bmatrix} \] is singular for the following values of \(x\).