I'm sorry, but that's not how that works. Your example is of a second-degree equation, which can't be solved by linear algebra. Linear algebra was invented to

I'm sorry, but that's not how that works. Your example is of a second-degree equation, which can't be solved by linear algebra. Linear algebra was invented to solve systems of linear equations, and matrices first arose as a convenient notation for expressing those. Matrix multiplication came later and is now understood to correspond to the composition of linear morphisms on vector spaces. If you try to extend the (very few) methods we have for obtaining exact solutions to polynomial equations in one variable to higher dimension, you (a) fail and (b) invent algebraic geometry.