JEE MAIN Matrices Previous Year Questions (PYQs) – Page 2 of 15

Let $A = \left[ {\matrix{ 1 & 2 \cr { - 1} & 4 \cr } } \right]$. If A^$-$1 = $\alpha$I + $\beta$A, $\alpha$, $\beta$ $\in$ R, I is a 2 $\times$ 2 identity matrix then 4($\alpha$ $-$ $\beta$) is equal to :

The system of equations $\begin{cases} x+y+z=6,\\ x+2y+5z=9,\\ x+5y+\lambda z=\mu \end{cases}$ has no solution if:

If $A=\dfrac12\begin{bmatrix}1 & \sqrt{3}\\ -\sqrt{3} & 1\end{bmatrix}$, then:

Let $A=\left[a_{i j}\right]$ be a $3 \times 3$ matrix such that $A\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], A\left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]$ and $A\left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$, then $a_{23}$ equals :

$ \text{Let the minimum value } v_{0} \text{ of } v=\lvert z\rvert^{2}+\lvert z-3\rvert^{2}+\lvert z-6i\rvert^{2},\ z\in\mathbb{C} \text{ be attained at } z=z_{0}. \text{ Then } \lvert 2z_{0}^{2}-\overline{z_{0}}^{\,3}+3\rvert^{2}+v_{0}^{2} \text{ is equal to:} $

Let $A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ and $B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2+\ldots+(\operatorname{adj} A)^{10}$. Then, the sum of all the elements of the matrix

If the system of equations $x + y + a z = b$ $2x + 5y + 2z = 6$ $x + 2y + 3z = 3$ has infinitely many solutions, then $2a + 3b$ is equal to :

Let $A$ be a matrix such that $A \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$ is a scalar matrix and $|3A| = 108$. Then $A^2$ equals :

Let $\theta = {\pi \over 5}$ and $A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$. If B = A + A⁴, then det (B) :

Let $A=\begin{pmatrix} 0 & 2q & r\\ p & q & -r\\ p & -q & r \end{pmatrix}$. If $AA^{T}=I_{3}$, then $|p|$ is :