1. Add, Subtract, and Multiply Matrices

2. A matrix M is an array of cell entries (m row,column ) that have rectangular dimensions (Rows x Columns). Example: 3x4 3 4 15x Dimensions: A a row,column A Matrix

3. Scalar Multiplication Every entry in the matrix is multiplied by the number outside the matrix (scalar). Example:

4. Matrix Addition/Subtraction IF the matrices have the same dimensions, add or subtract corresponding cell entries. Examples: b+h

5. Matrix Addition/Subtraction Perform the indicated operation: The matrices MUST have the same dimensions!

6. Matrix Multiplication 2x3 3x2 1 1 2 2 15 16 20 27 2x2 1 Multiply the elements of each row of the first matrix by the elements of each column in the second matrix. 2 Add the products. 3 The answer goes into a row of 1st, column of 2nd. a 1,1 a 1,2 a 2,1 a 2,2

7. Matrix Multiplication Can we multiply these… ? 2x3 2x2 3x4 5x1 1x3 3x2 # of columns in 1 st MUST be the same as # of rows in 2 nd ! No Yes

8. Matrix Multiplication with a Context CarsTrucks Bull’s Eye Order JC Nickels Department Store Order Cars Trucks WheelsSeatsGas Tanks Bull’s Eye Total Order JC Nickels Department Store Total Order Wheels Seats Gas Tanks

9. Matrices and the Calculator Follow the link below for instructions: http://www.cpm.org/pdfs/stuRes/A2C/chapte r_07/7.3.3A.pdf

10. Order in Matrix Multiplication Matters OR

11. Matrix Multiplication (a) (b) (c) (d) 3x3 1x33x31x3 2x2 3x33x1 2 2 33 1 1 3 3 3 3 33 22 1 1 The dimensions of a product of matrices are the # of rows of the first matrix by the # of columns of the second matrix. In order to multiply matrices, the # of columns in 1 st matrix MUST be the same as # of rows in 2 nd Matrix.