How are matrices related to vectors? I know it's a silly question, but there's something I feel like I'm missing in my understanding of matrices. 
I'm studying linear algebra, and much of what we covered in the first few topics related to vectors (vector spaces, linear independence, etc.), but then all of a sudden we started using matrices, loosely defining them as an "array of numbers". 
So I'm kind of confused, is a matrix supposed to be a list of vectors? And if so, are they the rows or the columns of the matrix? 

A vector is a linear array of quantities.
A matrix is a 2-dimensional array of quantities.
Three dimensional and higher dimensional arrays also exist, they are called Tensors.
A matrix can be thought of a sequence of column vectors, but also as a sequence of row vectors, both interpretations are useful.
 An example of an important theorem in this regard is :row rank=column rank.
