3.6 systems and matrices[1]
- 1. 3.6 SOLVING SYSTEMS USING MATRICES
- 2. MATRICES A matrix is a rectangular array of numbers, displayed within brackets. 2 4 1 A= 6 5 3 The dimensions of a matrix are the numbers of rows by the numbers of columns in the array.
- 3. MATRICES Each number in a matrix is a matrix element and can be identified by its row and column number Example: a11 a12 a13 A= a21 a22 a23
- 4. EXAMPLE: IDENTIFYING A MATRIX ELEMENT What is element a23 in matrix A? 4 −9 17 1 A= 0 5 8 6 −3 −2 10 0
- 5. SYSTEMS OF EQUATIONS AND MATRICES We can represent systems of equations as matrices Each row represents an equation Each column represents the coefficients of a variable Example:
- 7. EXAMPLE: REPRESENT THE SYSTEM WITH A MATRIX x − 3y + z = 6 x + 3 z = 12 y = −5 x + 1
- 8. EXAMPLE: WRITE THE SYSTEM OF EQUATIONS REPRESENTED BY THE MATRIX 5 2 7 0 1 9
- 9. SOLVING A SYSTEM USING A MATRIX We can solve a system by using a matrix and performing row operations Row Operations are the “legal moves and manipulations” we can make in a matrix Solving a system using row operations is similar to elimination, because we use the same steps, but don’t have variables
- 10. SOLVING A SYSTEM USING MATRICES Row Operations: Switch any two rows Multiply a row by a constant Add (subtract) one row to another row Make sure you write down what you are doing!
- 11. SOLVING A SYSTEM USING MATRICES Goal:To use row operations to get a matrix in the following forms: 1 0 0 a 1 0 a or 0 1 0 b 0 1 b 0 0 1 c Matricesthat represent the solution of a system are in reduced row echelon form.
- 12. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX x + 4 y = −1 2 x + 5 y = 4
- 13. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX 9 x − 2 y = 5 3 x + 7 y = 17
- 14. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX x + 2 y = 16 3 x + y = 8
- 15. ASSIGNMENT Page 179 #8 – 11, 13 – 23 odd, 24, 27 – 29
- 16. 3.6 SOLVING SYSTEMS USING MATRICES Part 2 – Three- Variable Systems
- 17. USING MATRICES FOR THREE VARIABLE SYSTEMS Same goal and row operations used to solve a system with two variables
- 18. SOLVING A SYSTEM USING MATRICES Row Operations: Switch any two rows Multiply a row by a constant Add (subtract) one row to another row Make sure you write down what you are doing!
- 19. SOLVING A SYSTEM USING MATRICES Goal:To use row operations to get a matrix in the following forms: 1 0 0 a 1 0 a or 0 1 0 b 0 1 b 0 0 1 c Matricesthat represent the solution of a system are in reduced row echelon form.
- 20. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX
- 21. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX
- 22. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX
- 23. ASSIGNMENT 3.6 Worksheet