Linear Algebra and Quadratic Equations I'm just wondering if Linear Algebra is concerned only with Linear equations? Can quadratic equations(or any higher power) also be considered under Linear Algebra? What does the term Linear stand for?
 A: To start with an example, consider the vector space $\mathbb{R}^2$. We can consider polynomials in $\mathbb{R}[x]$, and for such a polynomial $f \in \mathbb{R}[x, y]$, we can consider its zero-set $Z = \{ (a, b) \in \mathbb{R}^2 | f(a, b) = 0 \}$. This is the set of coordinates satisfying the equation $f(a, b) = 0$. If $f$ is of the form $ax + by + c$ (a linear function), then the set $Z$ cuts out a line or a point or a subspace. We are of course justified in calling a line linear. But so is a plane called linear- it does not bend or have sharp cuts, the midpoint of any two points contained in it is contained in it, etc. Linear doesn't stand for anything here, but it matches everyday intuition about the word. 
On the other hand, if $f$ is some polynomial like $x^2 - y$, then the zero-set $Z$ above is a parabola. It has a curve to it. We wouldn't want to call something quadratic like that linear. Instead general equations like these fall within the purview of algebraic geometry. That subject generalizes first from $\mathbb{R}[x, y]$ to $k[x_1, ..., x_n]$ for any algebraically closed field $k$, and from there it makes a generalization to include a geometry for every commutative ring.
In this sense, quadratic equations and even higher degree equations are still of interest, but instead fall within the scope of other subjects (that's not to say quadratic things don't arise as tools sometimes to study the linear things, such as with quadratic forms).
A: Linear algebra very much  included Quadratic equations. in fact. Polynomial equations of any degree.  For example $ax^2+bx+c=0$ may be written as product of a row vector $(a, b, c)$ with a column vector $(x^2,x,1)^\top$.
