Determine Whether The Equation Is Linear In $x_1, x_2, $ And $x_3$
According to the book I'm using, the following are linear equations:
$$x_1 + 5x_2 – \sqrt{2x_3} = 1$$
$$ \pi x_1 – \sqrt{2x_2} + \frac{1}{3}x_3 = 7^{\frac{1}{3}}$$
The book also states:
a linear equation does not involve any products or roots of variables
What am I missing?
The exercise from the book, Elementary Linear Algebra by Howard Anton/ Chris Rorres:
Best Answer
For all I know, those equations, as they are written, are nonlinear. What the book states corresponds to my knowledge. It does seem strange that those equations are given as linear. Maybe what the book says is the first one is linear in $x_1,x_2$ but not $x_3$ and the second is linear in all variables but $x_2$? That's what I would say. Another possibility is that the root does not include the variable, in both cases. In that case, they would be linear in all variables. Anyway if there is a product, power, root, logarithm or any other function of variables that is not a coefficient times a single variable, the equation is not linear. That, at least, is what I know.