You & maths

Exercise Set 1.1 – No. 1

1. In each part, determine whether the equation is linear in x1x2 and x3.

\large {\color{Blue} (a)\; x_1+5x_2-\sqrt{2}x_3=1}

Notice that the equation contain \large {\color{blue} \sqrt2}, but it is only a constant in front of the variable x3.

All the variables have powers 1, and the are no combinations of variables such as x1.x2, so given equation is linear.

\large {\color{blue} (b) \; x_1+3x_2+x_1.x_3=2}

The equation contain term x1.x3 which is a product of two different variables, so it is not linear.

\large {\color{blue} (c) \; x_1=-7x_2+3x_3}

Given equation can be written as: 

\large {\color{blue} \; x_1+7x_2-3x_3=0}

So, it is linear.

\large {\color{blue} (d) \; x_1^{-2}+x_2+8x_3=5}

Given equation contains term \large {\color{blue} \; x_1^{-2}}. Since the power of the variable x1 is -2. Equation is not linear.

\large {\color{blue} (e) \; x_1^{{\frac{3}{5}}}-2x_2+x_3=4}

Given equation contains term \large {\color{blue} x_1^{{\frac{3}{5}}}}. Since the power of the variable x1 is \large {\color{blue} {{\frac{3}{5}}}}. Equation is not linear.

\large {\color{blue} (f) \; \pi x_1-\sqrt{2}x_2=7^{\frac{1}{3}}}

Given equation is linear. Same explanation as in part a)