Matrix. Operations with matrices. The inverse matrix. Determinants and their properties. Systems of linear equations

Theoretical questions:

1. The concept of matrix;

2. Matrix operations: addition of matrices, multiplication of a matrix by a number, matrix multiplication;

3. Calculating determinants of 2×2 and 3×3 matrices;

4. Solving systems of linear equations matrix method;

5. Solving systems of linear equations on Cramer's rule;

6. Investigation compatible system;

7. Solving systems of linear equations Gauss's method.

Classroom assignments:

1. Matrixes and are given. Find 3А+2В.

2. Find matrix Х, if:

3. Calculate: а) ;

б) АВ, if: .

4. Calculate АВ and ВА, if:

5. Calculate D= ABC-3E, if:

6. Find the values ​​of matrix polynomials:

а) , если

б)

в)

7. Calculate determinants:

8. Prove that , if

9. Solve systems of linear equations matrix method by matrix method, by Cramer’s formula, investigate systems on compatibility, and solve them by Gauss's method:

a. b. c.

10. Investigate systems on compatibility and, in case of compatibility, solve them by Gauss's method:

a. b. c.

Homework.

Theoretical material: The simplest problem of analytic geometry. Equations of a straight line on a plane. Vectors.

Solve problems:

1.Calculate , if:

2.Find АВС, if:

3.Prove, that , if:

4.Solve systems of linear equations matrix method by matrix method and by Cramer’s formula:

a. b.

5. Investigate systems on compatibility and, in case of compatibility, solve them by Gauss's method:

Date: 2015-01-02; view: 1217