જો $A = \begin{bmatrix} x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0 \end{bmatrix}$ અને $\det(A^3) = 125$ હોય,તો $x =$

ધારો કે $A = \begin{bmatrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \end{bmatrix}$. જો $|A|^2 = 25$ હોય, તો $|\alpha|$ ની કિંમત શોધો.

સમીકરણ $\left| \begin{array}{ccc} x-1 & 1 & 1 \\ 1 & x-1 & 1 \\ 1 & 1 & x-1 \end{array} \right| = 0$ ના બીજ કયા છે?

જો $A_n = \begin{bmatrix} 1-n & n \\ n & 1-n \end{bmatrix}$ હોય,તો $|A_1| + |A_2| + \dots + |A_{2021}| = $

જો $\left|\begin{array}{ll}2017 & 2018 \\ 2019 & 2020\end{array}\right|+\left|\begin{array}{ll}2021 & 2022 \\ 2023 & 2024\end{array}\right|=2 k$ હોય,તો $k^3=$ . . . . . .

$\begin{aligned} & \text{જો }\left|\begin{array}{ccc}n^2 & (n+1)^2 & (n+2)^2 \\ (n+1)^2 & (n+2)^2 & (n+3)^2 \\ (n+2)^2 & (n+3)^2 & (n+4)^2\end{array}\right|=\Delta \text{અને } \\ & \left|\begin{array}{ccc}1 & -4 & 7 \\ -2 & 3 & -5 \\ 3 & x & -3\end{array}\right|=2 \Delta+1, \text{હોય તો} x=\end{aligned}$