1. Systems of Equations and Matrices Review of Matrix Properties Mitchell

2. What is a Matrix? A matrix is an ordered set of numbers listed rectangular form Usually named with a capital letter, such as A, B, or C Example. Let A denote the matrix A = This matrix A has three rows and four columns. We say it is a 3x4 matrix. We denote the element (entry) on the second row and fourth column with a2,4

3. Types of Matrices Square Matrix – Matrix with same number of rows and columns 3X3 Row Matrix – Matrix with only one row Column Matrix – Matrix with only one column Matrices of the same kind – Two matrices of the same size. Both matrices are 3X4

4. Equality and Addition/Subtraction of Matrices Two matrices are equal if… 1. They are the same size 2. Corresponding (matching in position) elements are equal To Add/Subtract Matrices… Simply add/subtract corresponding numbers. You can only add or subtract matrices if they are same type matrices.

5. Multiplication Scalar Multiplication Matrix Multiplication

6. Scalar Multiplication Example A = 2A = Explain: How did we get the matrix 2A? Multiply every element inside matrix A by 2

7. Now You Try: B = Calculate: 1. 2B 2. -3B 3. 10B

8. Check your Answers B = Calculate: 1. 2B 2. -3B 3. 10B 2B = -3B = 10B =

9. Matrix Multiplication Example 1 Matrix Multiplication Example 2

10. Step 1: Check the number of rows and columns The number of columns in matrix A must equal the number of rows in matrix B Matrix A is a 3 X 2 matrix. Matrix B is a 2 X 4 matrix. They can be multiplied. They make a 3X4 Matrix Matrix W is a 4 X 1 matrix. Matrix Y is a 1 X 4 matrix. They can be multiplied. They make a 4X4 Matrix Matrix M is a 4 X 4 matrix. Matrix N is a 3 X 3 matrix. – They cannot be multiplied… WHY NOT?

11. Step 2: Multiply row times column and add Multiply each entry in A (going from left to right) by the corresponding entry in B (going from top to bottom) and then add the results.

12. Now You try Can the two matrices be multiplied? If so multiply them. If not tell why. 1. 2.

13. Check your answers 1. No they cannot be multiplied. You cannot multiply a 1X3 matrix with a 2X1 matrix. The number of columns in the first doesn’t match the number of rows in the second matrix. 2. Yes they can be multiplied

14. Larger Matrices Remember to multiply each row by each column

15. Larger Matrices Continued Remember when you multiply the first row it makes the first row of the answer. When you multiply the second row it makes the second row of the answer

16. Now you try Multiply the two matrices 1. 2.

17. Check your answers 1. 2.

18. DO NOW DUE NOW: