The question asks which of the following equations is linear. Let's go through each equation to determine linearity:

1. Equation (A): $2x_1^2 + 3x_2^2 + 4x_3^4 = 5$

   • This is not linear because it contains terms like $x_1^2$, $x_2^2$, and $x_3^4$, which are powers higher than 1.

2. Equation (B): $\sqrt{3}x_1 - \sqrt{2}x_2 + x_3 = 5$

   • This equation is linear. Each variable $x_1$, $x_2$, and $x_3$ appears to the first power, and there are no non-linear functions applied to the variables (e.g., squares, square roots, cosines).

3. Equation (C): $\sqrt{5}x_1 + 5\sqrt{x_2} - x_3 = 1$

   • This is not linear because of the term $\sqrt{x_2}$, which introduces a non-linear element.

4. Equation (D): $2^2x_1 + \cos(x_2) + 4x_3 = 7$

   • This is not linear because of the cosine function, $\cos(x_2)$, which is a non-linear operation.

Conclusion:

The only linear equation is (B).

Would you like further details or have any questions?
Here are 5 related questions to explore further:

1. What are the general characteristics of a linear equation?
2. How does the presence of powers or roots affect the linearity of an equation?
3. Can trigonometric functions be part of a linear equation?
4. What is the difference between linear and non-linear terms?
5. How do we graphically represent linear versus non-linear equations?

Tip: In a linear equation, each variable is raised to the first power and is not involved in any non-linear operations (e.g., trigonometric, exponential, or logarithmic functions).