A 2 × 2 matrix whose elements are given by a_ij = $\dfrac{(i + 2j)^2}{2}$ is:

1. $\begin{bmatrix} \dfrac{3}{2} & \dfrac{5}{2} \ \space & \space \ 8 & 18 \end{bmatrix}$

2. $\begin{bmatrix} \dfrac{5}{2} & \dfrac{7}{2} \ \space & \space \ 8 & 18 \end{bmatrix}$

3. $\begin{bmatrix} \dfrac{9}{2} & \dfrac{15}{2} \ \space & \space \ 8 & 18 \end{bmatrix}$

4. $\begin{bmatrix} \dfrac{9}{2} & \dfrac{25}{2} \ \space & \space \ 8 & 18 \end{bmatrix}$

If $\begin{bmatrix} 5 & 3 \ x & 7 \end{bmatrix} = \begin{bmatrix} y & z \ 1 & 7 \end{bmatrix}$, then the value of (x + y + z) is:

1. 9

2. 8

3. 11

4. 10

Which of the following statements is true for the transpose of a matrix?

1. The number of rows is same as that of the given matrix.

2. The number of columns is same as that of the given matrix.

3. The order is same as that of the given matrix.

4. The number of elements is same as that of the given matrix.

If $\begin{bmatrix} x + y \ x - y \end{bmatrix} = \begin{bmatrix} 8 \ 4 \end{bmatrix}$, then the value of xy is:

1. 4

2. 8

3. 10

4. 12