Watch Karpathy's recent lectures. They're gold. Start here[1] with micrograd[2]. It doesn't use linear algebra/matrices to start, but the principles are the same. The matrix multiplication is how the weights of the connections between neurons and the input values are combined (to form an activation value that then may lead to that neuron "firing" or not, depending on whether it passes some threshold function). We use matrices to model the connections between neurons - each row is a connection, and each column is a weight corresponding to an input.
I cannot speak to the author of the content of this github repo, but it appears they have completed the course and included all of the solutions here. It might let you jump right to what you're looking for.