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 3À+2Â.
2. Find matrix Õ, if:
3. Calculate: à) ;
á) ÀÂ, if: .
4. Calculate ÀÂ and ÂÀ, if:
5. Calculate D= ABC3E, if:
6. Find the values of matrix polynomials:
à) , åñëè
á)
â)
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 ÀÂÑ, 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: 20150102; view: 1031
