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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 3+2.

2. Find matrix , if:

3. Calculate: ) ;

) , if: .

4. Calculate and , if:

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

6. Find the values ​​of matrix polynomials:

) ,

)

)

7. Calculate determinants:

8. Prove that , if

9. Solve systems of linear equations matrix method by matrix method, by Cramers 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 , if:

3.Prove, that , if:

4.Solve systems of linear equations matrix method by matrix method and by Cramers formula:

a. b.

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

 


Date: 2015-01-02; view: 610


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