The most initial and one of the most difficult mathematical disciplines has very many dirty tricks. But it is not so difficult to pass examination in it: it is necessary to refresh knowledge gained during a semester in memory.
Instruction
1. Linear algebra, as a rule, it ""introduction discipline"" in further studying mathematical sciences. Studying the simplest concepts, but at the same time the most important begins with it. In this regard it is worth beginning preparation for examination with repetition of the subject ""Matrixes and Operations over Them"". It is important to remember properties of addition and multiplication. They in many respects simplify life at the solution of certain tasks.
2. Repeat everything that is connected with matrix determinant. Here special attention needs to be paid on properties as with their help you will be able to find determinant of any matrix. But it is required to you at the solution of a practical task. To examination you should know Gauss's method. It is the basic in application to the solution of tasks. Its essence in quickly to find determinant of any matrix.
3. Further it is necessary to recollect such concepts as a minor and its algebraic additions. They lead to a matrix rank which is the greatest possible order of all minors, other than zero. This theory needs to be repeated because in tasks to tickets it is often necessary not only to count matrix determinant, but also to find its rank. By definition it is not rational to find it most often. Therefore the matrix by means of Gauss's method is usually led to a ""step"" look. And all minors which are other than zero and remain nonzero, and those that are equal to zero, remain zero.
4. The following section for repetition is the subject ""Return Matrix"". To find the return to initial - any task of each teacher. In this case it is necessary to remember the theorem of existence is as follows: if the determinant of a matrix is not equal to zero, then the return to it exists.
5. And the last that needs to be known to examination that to hand over it on positive assessment, is the system of the linear equations. The studied data on matrixes and actions over them will help you to accustom and here. All transformations which need to be carried out with the linear equations anyway submit to laws of matrix operations.