1. In each part, determine whether the equation is linear in ${{x}}_{{1}}$, ${{x}}_{{2}}$ and ${{x}}_{{3}}$.

Notice that the equation contain , but it is only a constant in front of the variable ${{x}}_{{3}}$.

All the variables have powers 1, and the are no combinations of variables such as ${{x}}_{{1}}{.}{{x}}_{{2}}$, so given equation is **linear**.

The equation contain term ${{x}}_{{1}}{.}{{x}}_{{3}}$ which is a product of two different variables, so it is **not linear.**

Given equation can be written as:

So, it is** linear.**

Given equation contains term . Since the power of the variable ${{x}}_{{1}}$ is -2. Equation is **not linear**.

Given equation contains term . Since the power of the variable ${{x}}_{{1}}$ is . Equation is **not linear**.

Given equation is l**inear. **Same explanation as in part a)