In pretty much any statistical model with more than a handful of parameters (and almost all machine learning models do require more than a handful of parameters!), those parameters are represented as vectors or matrices. Linear algebra (and multivariate calculus) then become very important for reasoning about those parameters, fitting the models, making predictions and so on.
The multivariate Gaussian distribution is a great example of this. It's probably the most fundamental and important distribution in statistics, and working with these distributions is pretty much pure linear algebra -- quadratic forms over vectors of parameters, eigendecompositions of covariance matrices etc.
Even for non-statistically-motivated data mining: any time you're optimising over a lot of parameters, it's likely that linear algebra (and, as before, multivariate calculus) will help. Linear algebra is as important to calculus over multiple variables, as plain old high-scool algebra is to plain old univariate calculus.
The multivariate Gaussian distribution is a great example of this. It's probably the most fundamental and important distribution in statistics, and working with these distributions is pretty much pure linear algebra -- quadratic forms over vectors of parameters, eigendecompositions of covariance matrices etc.
Even for non-statistically-motivated data mining: any time you're optimising over a lot of parameters, it's likely that linear algebra (and, as before, multivariate calculus) will help. Linear algebra is as important to calculus over multiple variables, as plain old high-scool algebra is to plain old univariate calculus.