1. Matrix Arithmetic

2. A matrix M is an array of cell entries (m row,column ) and it must 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 179 (b) 180 (a) 182 183 (b) 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.

9. Order in Matrix Multiplication Matters

10. Identity Matrix The product of a square matrix A and its identity matrix I, on the left or the right, is A. AI = IA =A General Form: I Must be a square matrix

11. Identity Matrix Example