Let's study an algorithm of finding of the return matrix by two main methods: by Gauss's method and by means of an allied matrix.
It is required to you
- - attentiveness
- - knowledge of a technique
Instruction
1. Let the matrix And some size be given. The return matrix of a matrix And will be the matrix of B at which multiplication by an initial matrix And the single matrix E will turn out. The return matrix can be found only for a square matrix which determinant is not equal to zero. The matrix of B is calculated as follows: 1. Since the very first element, we go on a line from left to right, for each element mentally we delete a line and a column which it enters, we calculate determinant of the remained matrix (value of a minor) and we write down it in a new matrix. BUT! If from an initial matrix we take the current element, consistently passing on lines, then in a new matrix we write down them already in a column. That is not all. 2. Signs of the received elements, starting with the first, will alternate through one is a rough formulation. If to speak precisely, then the sign is defined by expression-1 in degree of the sums of indexes of this element, that is the sum of the line number and a column in which it is located. In other words, the sign on opposite needs to be changed at the elements having the Odd sum of indexes.3. Before the received return matrix of B the coefficient 1 / is put (determinant of an initial matrix A).
2. It is only one of possible methods. It is also possible to use Gauss's method. It is that we take an initial matrix And yes at the same time we will take a single matrix of E. Primenyaya of transformation of lines or columns (we can read or put the corresponding columns or lines or to multiply them by number) to both of them And to E. Togda the second turned-out matrix will be the return, that is V.Proverit correctness of your calculations very simply: multiply an initial matrix And yes the return to it B matrix. If the single matrix E turns out, then all actions are made truly.