Linear algebra, as a rule, the "lead discipline" in the further study of mathematics. It begins with learning the simplest concepts, but at the same time, and the most important. In this regard, to start preparing for the exam is with the repetition of the theme "Matrixes and operations on them". It is important to remember the properties of addition and multiplication. In many ways they make life easier when solving certain tasks.
Repeat everything to do with the determinant of the matrix. Here, special attention should be paid to properties, as with their help you will be able to find the determinant of any matrix. But it will be useful in solving practical tasks. For the exam you definitely need to know the method of Gauss. He is the ultimate in applied to the solution of problems. Its essence is to quickly find the determinant of any matrix.
Next you need to recall concepts such as the minor and its algebraic Supplement. They lead to the rank of a matrix, which is the maximum possible order of all nonzero minors.
This theory need to be repeated, because the tickets frequently need not only to calculate the determinant of a matrix and find its rank. By definition, finding it are often not rational. Therefore the matrix using the method of Gauss generally result in a "step" form. And all the minors that are nonzero, and remain non-zero and those equal to zero, remain zero.
The next section to repeat is the theme of "Inverse matrix". Find back to the original - any task of each teacher. In this case, you need to recall a theorem on the existence of such: if the determinant of the matrix not equal to zero, the opposite to it exists.
And the last thing you need to know for the exam, to pass on positive feedback, is a system of linear equations. Studied data on matrices and operations on them to help you here. All transformations that need to hold with linear equations, or otherwise obey the laws of matrix operations.