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Let $\text{A}=\begin{bmatrix}1&0\\2&1\end{bmatrix},$ and $U_1, U_2$ are e first and second columns respectively of a $2 \times 2$ matrix $U.$ Also, let the column matrices $U_1$ and $U_2$ satisfying $\text{AU}_1=\begin{bmatrix}1\\0\end{bmatrix}$ and $\text{AU}_2=\begin{bmatrix}2\\3\end{bmatrix}.$ Based on the above information, answer the following questions.

1. The matrix $U_1 + U_2$​​​​​​​ is equal to:

1. $\begin{bmatrix}1\\-1\end{bmatrix}$
2. $\begin{bmatrix}2\\-2\end{bmatrix}$
3. $\begin{bmatrix}3\\-3\end{bmatrix}$
4. $\begin{bmatrix}4\\-4\end{bmatrix}$

2. The value of $|U|$ is:

1. $2$
2. $-2$
3. $3$
4. $-3$

3. If $\text{X}=\begin{bmatrix}3&2\end{bmatrix}\text{U}\begin{bmatrix}3\\2\end{bmatrix},$ then the value of $|X| =$

1. $3$
2. $-3$
3. $-5$
4. $5$

4. The minor of element at the position $a_{22}$ in $U$ is:

1. $1$
2. $2$
3. $-2$
4. $-1$

5. If $\text{U}=[\text{a}_\text{ij}]_{2\times2},$ then the value of $a_{11}A_{11 }+ a_{12}A_{12},$ where $A_{ij}$ denotes the cofactor of $a_{ij},$ is:

1. $1$
2. $2$
3. $-3$
4. $3$