IDZ Ryabushko 1.1 Option 4

No. 1. It is necessary to find minors and algebraic complements for a given determinant and calculate its value. To do this, perform the following steps:

• Let's find all the minors of the matrix, which are obtained by deleting a certain row and column from it.
• For each minor, we find the corresponding algebraic complement, which is defined as the product of (-1)^(i+j) by the value of the minor, where i and j are the row and column numbers, respectively.
• Let's calculate the determinant of the matrix: a) expanding it into the elements of the i-th row; b) decomposing it into elements of the j-th column; c) having previously received zeros in the i-th line. In this case i = 1, j = 3.

No. 2. Given two matrices A and B. You need to find:

• product of matrices A and B (AB);
• product of matrices B and A (BA);
• inverse matrix A (A⁻¹);
• the product of matrix A and its inverse (AA⁻¹);
• the product of the inverse matrix A and matrix A (A⁻¹A).

"IDZ Ryabushko 1.1 Option 4" is a digital product, which is a collection of problems for solving individual homework in mathematics, developed by the author Ryabushko. The collection includes problems on various topics, such as algebra, geometry, trigonometry and others.

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IDZ Ryabushko 1.1 Option 4 is a digital collection of mathematics problems developed by Ryabushko.

The collection includes problems on various topics, such as algebra, geometry, trigonometry and others. The beautiful HTML design of the product allows you to quickly and conveniently find the necessary tasks, familiarize yourself with the conditions and solutions, and also use materials to prepare for exams and tests.

The collection of problems is intended for schoolchildren and students studying mathematics, as well as for teachers and tutors who can use the problems to prepare pupils and students.

Answer to problem No. 1. For a given determinant, it is necessary to find minors and algebraic complements and calculate its value. To do this, you need to find all the minors of the matrix obtained by deleting a certain row and column. For each minor, we find the corresponding algebraic complement, which is defined as the product of (-1)^(i+j) by the value of the minor, where i and j are the row and column numbers, respectively. Then we calculate the determinant of the matrix by decomposing it into the elements of the i-th row, into the elements of the j-th column and first obtaining zeros in the i-th row. In this case i=1 and j=3.

Answer to problem No. 2. Given two matrices A and B. It is necessary to find: a) the product of matrices A and B (AB); b) the product of matrices B and A (BA); c) inverse matrix A (A⁻¹); d) the product of matrix A and its inverse (AA⁻¹); e) the product of the inverse matrix A and matrix A (A⁻¹A).

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IDZ (Individual Homework) "Ryabushko 1.1" option 4 is a linear algebra problem. The task requires the following steps:

1. Find minors and algebraic complements for a given determinant.
2. Calculate the determinant of the matrix: a) decomposing it into the elements of the i-th row; b) decomposing it into the elements of the j-th column; c) having previously received zeros in the i-th line, where i = 1, j = 3.
3. For two matrices A and B find: a) product AB; b) product BA; c) inverse matrix A; d) the product of matrix A and its inverse A⁻¹; e) the product of the inverse matrix A⁻¹ and the matrix A.

IDZ Ryabushko 1.1 Option 4 is an educational and methodological complex for preparing schoolchildren for the unified state exam in mathematics. IDH means "individual homework."

The complex includes tasks on various topics in mathematics, including algebra, geometry, trigonometry and calculus. Each task is accompanied by a detailed explanation and examples of solutions, which helps students better understand the material.

Option 4 differs from other options in the tasks that were selected by the authors of the complex to achieve maximum efficiency in preparing students for the exam.

Ryabushko IDZ 1.1 Option 4 is intended for 11th grade students and can be used both in school classes and for additional independent training at home.

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