1 / 30

Matrices

Matrices. Matrix - a rectangular array of variables or constants in horizontal rows and vertical columns enclosed in brackets. Element - each value in a matrix; either a number or a constant. Dimension - number of rows by number of columns of a matrix.

springfield
Download Presentation

Matrices

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. Matrices

  2. Matrix - a rectangular array of variables or constants in horizontal rows and vertical columns enclosed in brackets. Element - each value in a matrix; either a number or a constant. Dimension - number of rows by number of columns of a matrix. **A matrix is named by its dimensions.

  3. Examples: Find the dimensions of each matrix. Dimensions: 3x2 Dimensions: 4x1 Dimensions: 2x4

  4. Different types of Matrices • Column Matrix - a matrix with only one column. • Row Matrix - a matrix with only one row. • Square Matrix - a matrix that has the same number of rows and columns.

  5. Equal Matrices - two matrices that have the same dimensions and each element of one matrix is equal to the corresponding element of the other matrix. *The definition of equal matrices can be used to find values when elements of the matrices are algebraic expressions.

  6. Examples: Find the values for x and y * Since the matrices are equal, the corresponding elements are equal! * Form two linear equations. * Solve the system using substitution.

  7. 2. Set each element equal and solve!

  8. Matrix Operations • Addition • Subtraction • Multiplication • Inverse

  9. Addition

  10. Addition

  11. Addition Conformability To add two matrices A and B: • # of rows in A = # of rows in B • # of columns in A = # of columns in B

  12. Subtraction

  13. Subtraction

  14. Subtraction Conformability • To subtract two matrices A and B: • # of rows in A = # of rows in B • # of columns in A = # of columns in B

  15. Multiplication Conformability • Regular Multiplication • To multiply two matrices A and B: • # of columns in A = # of rows in B • Multiply: A (m x n) by B (n by p)

  16. Multiplication General Formula

  17. Multiplication I

  18. Multiplication II

  19. Multiplication III

  20. Multiplication IV

  21. Multiplication V

  22. Multiplication VI

  23. Multiplication VII

  24. Inner Product of a Vector • (Column) Vector c (n x 1)

  25. Outer Product of a Vector • (Column) vector c (n x 1)

  26. Inverse of 2 x 2 matrix • Find the determinant = (a11 x a22) - (a21 x a12) For det(A) = (2x3) – (1x5) = 1

  27. Inverse of 2 x 2 matrix • Swap elements a11 and a22 Thus becomes

  28. Inverse of 2 x 2 matrix • Change sign of a12 and a21 Thus becomes

  29. Inverse of 2 x 2 matrix • Divide every element by the determinant Thus becomes (luckily the determinant was 1)

  30. Inverse of 2 x 2 matrix • Check results with A-1 A = I Thus equals

More Related