How to solve matrices?
A mathematical matrix is a tableordered elements. The dimensions of this table are determined by the number of rows and columns in it. As for the solution of matrices, they are called the huge number of operations that are performed on these very matrices. Mathematicians distinguish several types of matrices. For some of them, general rules for the decision apply, but for others they do not work. For example, if the matrices have the same dimension, then they can be folded, and if they agree with each other, they can be multiplied. It is necessary to find a determinant for solving any matrix. In addition, the matrices are transposed and found in them minors. So, let's look at how to solve matrices.
The order of solving matrices
First, we write down the given matrices. We count how many rows and columns there are. If the number of rows and columns is the same, then such a 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 right lower corner to the upper left. The second diagonal in the matrix is secondary. Now we need to transpose the matrix. To do this, you must replace the elements of the rows in each of the two matrices with the corresponding column elements. For example, the element under a21 turns out to be an element of a12 or vice versa. Thus, after this procedure, a completely different matrix should appear.
If the matrices have exactly the samedimension, they can easily be folded. To do this, we take the first element of the first matrix a11 and add it to the similar element the second matrix b11. What happens as a result, we write down to the same position, only in a new matrix. Now we add all the other elements of the matrix in a similar way, until we get a completely different matrix. Let's see a few more ways to solve matrices.
Matrix Action Options
We can also determine whethermatched matrices. For 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 the element of a row of one matrix by a similar element of the column of the other matrix. Only after this it will be possible to calculate the amount of the resulting works. Proceeding from this, the initial element of the matrix, which should result as a result, is g11 = a11 * b11 + a12 * b21 + a13 * b31 + ... + a1m * bn1. After you add and multiply all the pieces, you can fill the resulting matrix.
Also, when solving matrices, it is possible to find themdeterminant 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 products of 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 the given element, you needdelete the column and row, where this element is located. Then find the determinant of this matrix. He will be the corresponding minor. Such a 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, it is not so difficult to solve matrices if you know the basic mathematical actions.
