# How to solve the matrix?

Mathematical matrix is a table of ordered elements. The size of this table is determined by the number of rows and columns in it. As for the solution of matrices, they are called a huge number of operations that are performed on these same matrices. Mathematicians distinguish several types of matrices. For some of them, the general rules on decision apply, while for others they do not. For example, if the matrices have the same dimension, then they can be added, and if they are consistent with each other, then they can be multiplied. Be sure to solve any matrix, you must find a determinant. In addition, the matrices are transposed and the minors are located in them. So let's consider how to solve matrices.

## The procedure for solving matrices

First we write the given matrices. We count how many rows and columns in them. If the number of rows and columns is the same, then this matrix is called square. If each element of the matrix is equal to zero, then such a matrix is zero. The next thing we do is find the main diagonal of the matrix.The elements of such a matrix are from the lower right to the upper left. The second diagonal in the matrix is a secondary one. Now you need to transpose the matrix. To do this, in each of the two matrices it is necessary to replace the elements of the rows with the corresponding elements of the columns. For example, the element under a21 will be the element a12 or vice versa. Thus, after this procedure, a completely different matrix should appear.

If the matrices have exactly the same dimension, then they can be easily folded. To do this, we take the first element of the first a11 matrix and add it to the second matrix b11 with a similar element. We write down what we get as a result to the same position, only in the new matrix. Now, in the same way, we add up all the other elements of the matrix, until a new completely different matrix is obtained. Let's see some more ways to solve matrices.

## Variants of actions with matrices

We can also determine if matrices are consistent. To do this, we need to compare the number of rows in the first matrix with the number of columns of the second matrix. If they are equal, you can multiply them. To do this, we multiply in pairs the element of a row of one matrix by a similar element of the column of another matrix. Only after that it will be possible to calculate the amount of the resulting works. Proceeding from this, the initial element of the matrix that should be the result will be equal to g11 = a11 * b11 + a12 * b21 + a13 * b31 + ... + a1m * bn1. After the addition and multiplication of all works will be performed, you will be able to fill in the final matrix.

It is also possible, when solving matrices, to find their determinant and determinant for each. If the matrix is square and has a dimension of 2 by 2, then the determinant can be found as the difference of all the products of the elements of the main and secondary diagonals. If the matrix is already three-dimensional, then the determinant can be found by applying the following formula. D = a11 * a22 * a33 + a13 * a21 * a32 + a12 * a23 * a31 - a21 * a12 * a33 - a13 * a22 * a31 - a11 * a32 * a23.

To find the minor of a given element, you need to cross out the column and row where the element is located. After that, find the determinant of this matrix. He will be the corresponding minor. A similar method of solving matrices was developed several decades ago in order to increase the reliability of the result by dividing the problem into sub-problems.Thus, solving matrices is not so difficult if you know the basic mathematical operations.

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