As practice do (or know that you could easily do) the following exercises/problems from the class textbook “3000 Solved Problems in Linear Algebra”. Show all your reasoning as you would in a quiz.

Note that different notation for vectors may be used but the intent is the same: a vector is a tuple of real numbers written in some way in the above book, conventionally written as a column vector in class for layout consistency with a system of linear equations written one equation per line. Sometimes where in class we would write x for a column vector the book may write it not in bold or as X as it is a matrix with one column, after defining what it is. Follow the class conventions to the extent it is convenient to you. Provided we understand what you are communicating and hence your reasoning in a quiz, we will interpret notation as transparently as possible. Of course it is safest to stick to the systematic use of notation used in lecture, and this may help you too.