1 / 24

Matrix Algebra

Precalculus. Lesson 7.2. Matrix Algebra. Quick Review. What you’ll learn about. Matrices Matrix Addition and Subtraction Matrix Multiplication Identity and Inverse Matrices Determinant of a Square Matrix Applications … and why

suki
Télécharger la présentation

Matrix Algebra

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. Precalculus Lesson 7.2 Matrix Algebra

  2. Quick Review

  3. What you’ll learn about • Matrices • Matrix Addition and Subtraction • Matrix Multiplication • Identity and Inverse Matrices • Determinant of a Square Matrix • Applications … and why Matrix algebra provides a powerful technique to manipulate large data sets and solve the related problems that are modeled by the matrices.

  4. Matrix

  5. Matrix Vocabulary Each element, or entry, aij, of the matrix uses double subscript notation. The row subscript is the first subscript i, and the column subscript is j. The element aij is the ith row and the jth column. In general, the orderof anm × n matrix is m×n.

  6. Example Determining the Order of a Matrix

  7. Matrix Addition and Matrix Subtraction

  8. Example Matrix Addition

  9. Example Using Scalar Multiplication

  10. The Zero Matrix Example:

  11. Additive Inverse

  12. Example Using Additive Inverse

  13. Matrix Multiplication

  14. Example Matrix Multiplication

  15. Identity Matrix

  16. Inverse of a Square Matrix

  17. Example Inverse of a Square Matrices Yes

  18. Inverse of a 2 × 2 Matrix

  19. Determinant of a Square Matrix Refer to text pg 583

  20. Inverses of n× n Matrices An n × n matrix A has an inverse if and only if detA ≠ 0.

  21. Example Finding Inverse Matrices

  22. Properties of Matrices Let A, B, and C be matrices whose orders are such that the following sums, differences, and products are defined. 1. Commutative property Addition: A + B = B + A Multiplication: Does not hold in general 2. Associative property Addition: (A + B) + C = A + (B + C) Multiplication: (AB)C = A(BC) 3. Identity property Addition: A + 0 = A Multiplication: A·In = In·A = A

  23. Properties of Matrices Let A, B, and C be matrices whose orders are such that the following sums, differences, and products are defined. 4. Inverse property Addition: A + (-A) = 0 Multiplication: AA-1 = A-1A = In |A|≠0 5. Distributive property Multiplication over addition: A(B + C) = AB + AC (A + B)C = AC + BC Multiplication over subtraction: A(B - C) = AB - AC (A - B)C = AC - BC

  24. Homework: Text pg588/589 Exercises #2, 4, 14, 20, 24, and 34

More Related