Содержание
- 2. Ch1_ Ch1_ Definition An equation such as x+3y=9 is called a linear equation (in two variables
- 3. Ch1_ Ch1_ Definition A linear equation in n variables x1, x2, x3, …, xn has the
- 4. Ch1_ Ch1_ Solutions for system of linear equations Figure 1.1 Unique solution x + 3y =
- 5. Ch1_ Ch1_ A linear equation in three variables corresponds to a plane in three-dimensional space. ※
- 6. Ch1_ Ch1_
- 7. Ch1_ Ch1_ A solution to a system of a three linear equations will be points that
- 8. Ch1_ Ch1_ Definition A matrix is a rectangular array of numbers. The numbers in the array
- 9. Ch1_ Ch1_ Submatrix Row and Column
- 10. Ch1_ Ch1_
- 11. Ch1_ Ch1_ matrix of coefficients and augmented matrix Relations between system of linear equations and matrices
- 12. Ch1_ Ch1_ Elementary Transformation Interchange two equations. Multiply both sides of an equation by a nonzero
- 13. Ch1_ Ch1_ Example 1 Solving the following system of linear equation.
- 14. Ch1_ Ch1_
- 15. Ch1_ Ch1_ Example 2 Solving the following system of linear equation. Solution
- 16. Ch1_ Ch1_ Example 3 Solve the system Solution
- 17. Ch1_ Ch1_ Summary Use row operations to [A: B] : Def. [In : X] is called
- 18. Ch1_ Ch1_ Example 4 Many Systems Solving the following three systems of linear equation, all of
- 19. Ch1_ Ch1_ Homework Exercises will be given by the teachers of the practical classes.
- 20. Ch1_ Ch1_ 1.2 Gauss-Jordan Elimination Definition A matrix is in reduced echelon form if Any rows
- 21. Ch1_ Ch1_ Examples for reduced echelon form (✓) (✓) (?) (?) elementary row operations,reduced echelon form
- 22. Ch1_ Ch1_ Gauss-Jordan Elimination System of linear equations ⇒ augmented matrix ⇒ reduced echelon form ⇒
- 23. Ch1_ Ch1_ Example 1 Use the method of Gauss-Jordan elimination to find reduced echelon form of
- 24. Ch1_ Ch1_ Example 2 Solve, if possible, the system of equations Solution The general solution to
- 25. Ch1_ Ch1_ Example 3 Solve the system of equations Solution ⇒ many sol.
- 26. Ch1_ Ch1_ Example 4 Solve the system of equations Solution
- 27. Ch1_ Ch1_ Example 5 This example illustrates a system that has no solution. Let us try
- 28. Ch1_ Ch1_ Homogeneous System of linear Equations Definition A system of linear equations is said to
- 29. Ch1_ Ch1_ Homogeneous System of linear Equations Note. Non trivial solution
- 30. Ch1_ Ch1_ Homework Exercise will be given by the teachers of the practical classes.
- 31. Ch1_ 1.3 Gaussian Elimination Definition A matrix is in echelon form if Any rows consisting entirely
- 32. Ch1_ Example 6 Solving the following system of linear equations using the method of Gaussian elimination.
- 33. Ch1_ The corresponding system of equation is
- 34. Ch1_ Example 7 Solving the following system of linear equations using the method of Gaussian elimination,
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