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List of top Engineering Mathematics Questions on Linear Algebra asked in GATE PE

Let $\mathbf{X}=\begin{bmatrix} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33} \end{bmatrix}$ be a $3\times 3$ matrix. The determinant of $\mathbf{X}$ is $5$. The determinant of matrix $\mathbf{Y}=\begin{bmatrix} x_{11} & x_{12} & x_{13} \\ 2x_{21} & 2x_{22} & 2x_{23} \\ 3x_{31} & 3x_{32} & 3x_{33} \end{bmatrix}$ is __________.
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