Though a bit of an exaggeration, it can

Though a bit of an exaggeration, it can be said that a mathematical problem
can be solved only if it can be reduced to a calculation in linear algebra.
And a calculation in linear algebra will reduce ultimately to the solving of
a system of linear equations, which in turn comes down to the manipulation
of matrices. Throughout this text and, more importantly, throughout
mathematics, linear algebra is a key tool (or more accurately, a collection
of intertwining tools) that is critical for doing calculations.