If your name is Neo, and you can see through the matrix or are you a student Zealand or other similar authors, and can take the answers and solutions to problems of space options, the more you can not read. If you are unfamiliar with need to solve the problem using matrices and are confident that never encounter, then this article is also not for you. But if you are enrolled in high school and you have a course of higher mathematics, we face a decision problems where you must use the calculation with matrices, you somehow have to. This problem affects some already in school. At first glance it might seem that the operations on matrices are simple and easy solved, but when the dimension of the matrix than three by three, then the problems begin. But the main problem is that it's boring and tedious process.
For example, we need to check the consistency of a system of four linear equations by the theorem of Kronecker-Capelli, what we need to compute the rank of major and rank of the augmented matrix. To calculate the rank of four by four should do fifteen operations, and since these operations, there is division, we have to deal with fractions. But we need to calculate and rank of the augmented matrix, then multiply by fifteen to thirty two and get operations. It is necessary to note that the equations can be more. And in so many calculations to make an annoying bug is fairly simple. Can take another example, consider the determinant of five on five, which means to reduce the matrix to triangular form, and multiply the main diagonal elements, it should not be forgotten that the determinant sign under permutation of rows is reversed. Total thirty-five operations without considering the permutation of rows and change the sign.
In fact, actually it's not even much in comparison to finding the inverse matrix by cofactors. That's where the real horror begins. Thus, we consider finding the inverse matritsyrazmernostyu four by four through cofactors. The first thing we find the determinant of a matrix that would ensure that the inverse matrix exists. This fifteen operations. After that, we find sixteen to nine cofactors operations and obtain one hundred forty-four operations and the total amount of one hundred fifty-nine operations! Now imagine that you make a mistake, how long it takes, that would find her, and nerves of steel there are necessities. What is there to say even simple operations such as transposition, addition, subtraction, multiplication of the number can spoil your mood. But this is not the whole list of operations, the matrix can still be multiplied by each other, to build a degree, etc. But all is not so bad, the Internet has resources that make all the calculations are online, as a result of you not only get answers to all the required operations, but also a detailed step by step solution, which is very convenient. You can only enter the initial data. Even if you want to learn themselves do all operations with matrices, it never hurts to double check your decision.