My First Instinct: Sledgehammer

I have an applied mathematics class wherein the professor has promised little of the math we will need is more advanced that a solid grasp of basic matrix algebra, its meaning, and what it is doing.

Yet whenever he asks for a solution to a problem (despite his prior assurance an elementary solution exists), I consistently throw out a more advanced concept. He asks for how to check the invertability of a matrix, I say determinants. He asks for how to compute the inverse, I say the adjoint. He says make an orthogonal matrix, I say pick some vectors and run Graham-Schmitt.

Pretty often I'm getting "That's way too complicated for what we need".

I think there's a theme here.