By EasyHow

How to pass linear algebra

The initial and one of the most difficult mathematical disciplines has very many pitfalls. But to pass the exam it is not so difficult: you need to brush up on the knowledge gained during the semester.

How to pass linear algebra
How to pass higher maths
How to pass an algebra test
How to calculate the determinant of a matrix

Instruction

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.

Note

1) the Multiplication of two matrices sometimes causes difficulties, especially if a long time with this operation did not work. So be sure to try and remember how to correctly multiply two matrices.

2) All the theorems that have been studied during the passage of linear algebra, you need to know with evidence. In most cases, the exams the teachers are not asking the theory itself, which is not so much, namely, evidence and understanding of the theorems.

Useful advice

1) Try not to forget that under the transposition of the parity of the permutation changes.

2) Remember that the transpose is a transformation in which each row becomes a column.

3) the Determinant of a matrix does not change if any row subtract any other, were multiplied by an arbitrary real number.

4) the Determinant of a matrix is equal to the sum of all the elements of an arbitrary line were multiplied by their cofactors.

5) All the elementary transformations that convert the system of linear equations in a system are equivalent.