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1. 已知 $\begin{vmatrix}a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33}\end{vmatrix} = c$ ,代数余子式之和 $\sum\limits_{i=1}^{3}\sum\limits_{j=1}^{3} A_{ij} = 3c$ ,则 $\begin{vmatrix}a_{11}+1 & a_{12}+1 & a_{13}+1 \\a_{21}+1 & a_{22}+1 & a_{23}+1 \\a_{31}+1 & a_{32}+1 & a_{33}+1\end{vmatrix} =$ \_\_\_\_\_\_\_\_\_\_.
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1. ([[线代2022秋B]]·1)已知 $\begin{vmatrix}a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33}\end{vmatrix} = c$ ,代数余子式之和 $\sum\limits_{i=1}^{3}\sum\limits_{j=1}^{3} A_{ij} = 3c$ ,则 $\begin{vmatrix}a_{11}+1 & a_{12}+1 & a_{13}+1 \\a_{21}+1 & a_{22}+1 & a_{23}+1 \\a_{31}+1 & a_{32}+1 & a_{33}+1\end{vmatrix} =$ \_\_\_\_\_\_\_\_\_\_.
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2. ([[线代2013秋A]]·4)已知向量空间 $V=\{(2a,2b,3b,3a)|a,b\in\mathbb{R}\}$,则 $V$ 的维数是\_\_\_\_\_.
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