A linear algebra point of view can be useful for some topics normally addressed in a second-year calculus course. Understanding jacobians and doing some things with systems of differential equations that require eigenvectors, etc.

Then in statistics, suppose you want to understand why the sum of squares of residuals in a simple linear regression problem has a scalar multiple of a chi-square distribution with $n-2$ degrees of freedom, where $n$ is the number of data points, and why it's independent of the estimate of the slope.  That all becomes clear if you know how a real symmetric matrix can be diagonalized by an orthogonal matrix.  Or suppose you want to understand why every non-negative definite symmetric real matrix can be realized as the variance of some random vector.  Same thing.