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This methodological guide will help you learn how to perform operations with matrices: addition (subtraction) of matrices, transposition of a matrix, multiplication of matrices, finding the inverse matrix. All the material is presented in a simple and accessible form, relevant examples are given, so even an unprepared person can learn to perform actions with matrices.
We have considered the actions of addition, subtraction and multiplication of matrices by a number. Another action on them is multiplication. It is more difficult to execute, and the rule itself may seem a little strange. When doing it, it is important to be able to determine the size of the matrices. Matrix multiplication is one of the most common matrix operations. The matrix that is obtained after multiplication is called the matrix product.
The process of matrix multiplication is possible only when the number of columns of the first matrix is equal to the number of rows of the second matrix. The matrix P can be multiplied by the matrix K only if the number of columns of the matrix P is equal to the number of rows of the matrix K. Matrices for which this condition is not satisfied cannot be multiplied. Quite often, you can find tasks with a trick, when the student is asked to multiply matrices, the multiplication of which is obviously impossible.
Matrix multiplication is performed by multiplying a row by a column. Finds the products of the first row element and the first column element, the second row element and the second column element, etc. Then the resulting works are summed up. In our calculator, you can find the product of matrices online for free with a detailed solution and even with complex numbers. We have available matrix-vector multiplication, multiplication of two matrices, product of square matrices and more.