Matrices

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Q JEE MAIN 2026

For some $\quad \alpha, \beta \in \mathbf{R}, \quad$ let $\quad A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right] \quad$ and $...

JEE Main Mathematics Hard

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Q JEE MAIN_2019_

If the system of linear equations $$ \begin{aligned} & x+y+z=5 \\ & x+2 y+2 z=6 \\ & x+3 y+\lambda z=\mu,(\lambda, \mu \in R), \text {...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

$...

JEE Main Mathematics Easy

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Q JEE Advanced 2025

Let $I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$ and $P=\left(\begin{array}{ll}2 & 0 \\ 0 & 3\end{array}\right)$. Let $Q=\left(\begin{array}{ll}x & y \\ z & 4\end{array}\right)$ for...

JEE Advance Mathematics Easy

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Q JEE MAIN 2019

If $B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1\end{array}\right]$ is the inverse of a $3 \times 3$ matrix $A$, then the...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $A+B=\left[\begin{array}{cc}2 & 3 \\ 5 & -1\end{array}\right]$, then $A B$ is...

JEE Main Mathematics Medium

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Q JEE-Advanced 2025

Consider the matrix $$ P=\left(\begin{array}{lll} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{array}\right) $$ Let...

JEE Advance Mathematics Easy

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Q JEE Main 2020

Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|A| \neq 0$. Consider the following two statements: (P) If $...

JEE Main Mathematics Hard

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Q JEE MAIN 2020

Let $A=\left\{X=(x, y, z)^{\top}: P X=0\right.$ and $\left.x^2+y^2+z^2=1\right\}$, where $...

JEE Main Mathematics Hard

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Q JEE MAIN 2020

Let $a, b, c \in R$ be all non-zero and satisfy $a^3+b^3+c^3=2$. If the matrix $$ A=\left(\begin{array}{lll} a & b & c \\ b &...

JEE Main Mathematics Medium

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Matrices