1 / 18

8.1 Matrices and Systems of Equations

8.1 Matrices and Systems of Equations. Let’s do another one:. we’ll keep this one. Now we’ll use the 2 equations we have with y and z to eliminate the y ’s. multiply the first equation by 8 and add the equations to eliminate y .

tana
Télécharger la présentation

8.1 Matrices and Systems of Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 8.1 Matrices and Systems of Equations

  2. Let’s do another one: we’ll keep this one Now we’ll use the 2 equations we have with y and z to eliminate the y’s.

  3. multiply the first equation by 8 and add the equations to eliminate y.

  4. Matrix: rectangular organization of real numbers in rows and columns Column 1 C 2 C 3 C n Row 1 Row 2 Row 3 Row m • Entry aijis a real number in a certain “i” row and “j” column

  5. Dimension, or ORDER, of a matrix • Dimension or order is given by m x n m = number of rows n = number of columns

  6. Square Matrix • In a square matrix: m = n; rows = columns • Note: To solve a system of equations, you will need square coefficient matrices

  7. Coefficient Matrix • A matrix whose real entries are the coefficients from a system of equations

  8. Solution Matrix • A column matrix whose entries are the solutions of the system of equations

  9. Augmented matrix- A matrix set up where the coefficient matrix and solution matrix of a system of equations is combinedNotation: Matrix square brackets with a bar separating the coefficients

  10. Augmented Matrix cont.’d

  11. Elementary Row Operations- Manipulating to Solve Matrices/ Systems 1.) Interchange two rows 2.) Multiply a row by a NONZERO multiple 3.) Add a multiplied row to another row

  12. Row- Echelon Form (ref) Page 548: 1.) If there is a row of all zeros, it is the last row 2.) The first nonzero entry of a nonzero row is 1 3.) The 1’s occur at a diagonal Reduced Row-echelon Form (rref) If every column that has a leading 1 has zeros above and below the 1.

  13. Page 548

  14. Gaussian Elimination 1.) Write the augmented matrix of a system of equations 2.) Use elementary row operations to rewrite the augmented matrix in ref form 3.) Rewrite the matrix as a system of equations and back-substitute in to solve for each variable

  15. Example 1: Solve Row 2: Added R1 + R2 -4 3 5 -1 3 -1 -3 0 -1 2 2 Row 3: Added -2(R1) + R3 -2 8 -6 -10 2 0 -4 6 0 8 -10 -4

  16. Row 3: Added 8(R2) + R3 0 -8 16 16 08 -10 -4 0 0 6 12 Row 3: 1/6(R2)

  17. No put back into a system of equations and back substitute

More Related