Basic Special Relativity can be studied without linear algebra. If you are interested in this approach, follow the Resnick book. If you master all of the material in Resnick, you will be able to do all the problems required for this course without linear algebra. However, this is not the recommended approach.
In the lectures, we will introduce 4-vectors (and perhaps tensors, if we have time). They are an essential component of Special Relativity (and later, of the advanced Electricity and Magnetism theory). Not only do they make the theory `beautiful', they make it much easier to solve problems in Special Relativity, especially those on energy and momentum conservation.
Therefore, in this class we will make an effort to master the 4-vector apparatus, and we will discuss its advantages in lectures and sections. Basic linear algebra is very helpful for this course; freshen up on matrix multiplication, determinants and inversion, if necessary.
We will also use matrix notation for some of the aspects of the Waves part of the course.
One of the previous TAs for this class Prasenjit Bose kindly provided materials for a linear algebra refresher:
For elementary introduction to the subject (which is as much as we need for the course), I found some of these youtube videos which does a very good job of walking someone through the basic operations of linear algebra.
Matrix multiplication review
Finding the inverse of a matrix review
How to find the determinant of a matrix
Finding Eigenvalues, Eigenvectors of a matrix and diagonalizing it
Same for 3x3 case