List of top Mathematics Questions on Linear Algebra asked in IIT JAM EN

Consider the matrix \( A = \begin{bmatrix} 4 & -1 \\ 12 & -3 \end{bmatrix} \).
The value of the determinant of \( A^5 \) is .......... (rounded off to two decimal places).

Let $x, y \in \mathbb{R}$ and the matrix \[ M = \begin{bmatrix} x + y & x - y \\ x - y & x + y \end{bmatrix}. \] Also, let $\text{adj}(M)$ be the adjoint and $\det(M)$ be the determinant of the matrix $M$. If \[ M \begin{bmatrix} 3 \\ 1 \end{bmatrix} = \begin{bmatrix} -1 \\ 3 \end{bmatrix}, \] then

Let $\|.\|$ and $\langle .,.\rangle$ denote the standard norm and inner product in $\mathbb{R}^n$, respectively. If $u, v \in \mathbb{R}^3$ such that $\|u\| = \|v\| = 2$ and the angle between $u$ and $v$ is $\pi/3$, then