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- 2. Barnett/Ziegler/Byleen Finite Mathematics 11e Addition and Subtraction of Matrices To add or subtract matrices, they must
- 3. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Addition Add the matrices
- 4. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Addition Solution Add the matrices Solution: First note that each matrix
- 5. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Subtraction Now, we will subtract the same two matrices =
- 6. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Subtraction Solution Now, we will subtract the same two matrices Subtract
- 7. Barnett/Ziegler/Byleen Finite Mathematics 11e Scalar Multiplication The scalar product of a number k and a matrix
- 8. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Scalar Multiplication Find (-1)A, where A =
- 9. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Scalar Multiplication Solution Find (-1)A, where A = Solution: (-1)A= -1
- 10. Barnett/Ziegler/Byleen Finite Mathematics 11e Alternate Definition of Subtraction of Matrices The definition of subtraction of two
- 11. Barnett/Ziegler/Byleen Finite Mathematics 11e Example The example on the right illustrates this procedure for two 2x2
- 12. Barnett/Ziegler/Byleen Finite Mathematics 11e Matrix Equations Example: Find a, b, c, and d so that
- 13. Barnett/Ziegler/Byleen Finite Mathematics 11e Matrix Equations Example: Find a, b, c, and d so that Solution:
- 14. Barnett/Ziegler/Byleen Finite Mathematics 11e Matrix Products The method of multiplication of matrices is not as intuitive
- 15. Barnett/Ziegler/Byleen Finite Mathematics 11e Arthur Cayley 1821-1895 Introduced matrix multiplication
- 16. Barnett/Ziegler/Byleen Finite Mathematics 11e Product of a Row Matrix and a Column Matrix In order to
- 17. Barnett/Ziegler/Byleen Finite Mathematics 11e Row by Column Multiplication Example: A row matrix consists of 1 row
- 18. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Revenue of a Car Dealer A car dealer sells four model
- 19. Barnett/Ziegler/Byleen Finite Mathematics 11e Solution using Matrix Multiplication We represent the number of each model sold
- 20. Barnett/Ziegler/Byleen Finite Mathematics 11e Matrix Product If A is an m x p matrix and B
- 21. Barnett/Ziegler/Byleen Finite Mathematics 11e Multiplying a 2x4 matrix by a 4x3 matrix to obtain a 2x3
- 22. Barnett/Ziegler/Byleen Finite Mathematics 11e Final Result
- 23. Barnett/Ziegler/Byleen Finite Mathematics 11e Undefined Matrix Multiplication Why is the matrix multiplication below not defined?
- 24. Barnett/Ziegler/Byleen Finite Mathematics 11e Undefined Matrix Multiplication Solution Why is the matrix multiplication below not defined?
- 25. Barnett/Ziegler/Byleen Finite Mathematics 11e Example Given A = B = Find AB if it is defined:
- 26. Barnett/Ziegler/Byleen Finite Mathematics 11e Solution Since A is a 2 x 3 matrix and B is
- 27. Barnett/Ziegler/Byleen Finite Mathematics 11e Is Matrix Multiplication Commutative? Now we will attempt to multiply the matrices
- 28. Barnett/Ziegler/Byleen Finite Mathematics 11e Practical Application Suppose you a business owner and sell clothing. The following
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