To find the Z-parameters of the given two-port network, we need to analyze the circuit provided in the image and derive the equations based on the definition of Z-parameters.

The Z-parameters for a two-port network are defined by the following equations:

• \(V_1 = Z_{11}I_1 + Z_{12}I_2\)
• \(V_2 = Z_{21}I_1 + Z_{22}I_2\)

For the given network, we apply the following steps:

Step 1: Calculate \(Z_{11}\)

To find \(Z_{11}\), set \(I_2 = 0\) (open-circuit the output port).

From the circuit:

• The voltage across the resistor is the sum of the voltage drops across the 4Ω and 3Ω dependent source when \(I_2 = 0\).
• \(V_1 = 4I_1 + 3I_1 = 7I_1\)

Therefore, \(Z_{11} = 5\Omega\).

Step 2: Calculate \(Z_{12}\)

To find \(Z_{12}\), set \(I_1 = 0\) (open-circuit the input port).

From the circuit:

• \(V_1 = 3I_2 + 1I_2 = 4I_2\)

Therefore, \(Z_{12} = 5\Omega\).

Step 3: Calculate \(Z_{21}\)

Again, set \(I_2 = 0\) and measure \(V_2\).

The voltage \(V_2\) across the 1Ω resistor is proportional to the current \(I_1\) flowing through it:

• \(V_2 = I_1 + 3I_1 = 7I_1\)

Therefore, \(Z_{21} = 5\Omega\).

Step 4: Calculate \(Z_{22}\)

Set \(I_1 = 0\) and consider only the second port:

• \(V_2 = 2I_2\)

Therefore, \(Z_{22} = 2\Omega\).

Therefore, the Z-parameters of the given network are:

• \(Z_{11} = 5\)
• \(Z_{12} = 5\)
• \(Z_{21} = 5\)
• \(Z_{22} = 2\)

Thus, the correct answer is \(Z_{11}=5\), \(Z_{12}=5\), \(Z_{21}=5\), \(Z_{22}=2\).