1. 2.2 Multiplying Matrices Mr. Anderson Pre Calculus Falconer Central High School Falconer, NY

2. Ordering a Matrix Hi. I’m calling to see if I could order a matrix, please. Why certainly.

3. Ordering a Matrix  (I, j) denotes the element in the i th row and the j th column.  Best to have an example of course.

4. Scalar Multiple  A scalar is a constant (a number).  The product of a scalar and a matrix is the result of “distributing” the scalar through the matrix.  Example

5. Multiplying Matrices  First, multiplication of matrices is not commutative.  Ie. ORDER MATTERS!!  Second, for two matrices to be multiplied, the number of columns in the first matrix must be equal to the number of rows in the second matrix.  In other words, matrices A and B can only be multiplied if A is an m x n matrix and B is an n x r matrix.

6. Multiplying Matrices (cont.)  In other words, matrices A and B can only be multiplied if A is an m x n matrix and B is an n x r matrix.  Furthermore, A  B will be an m x r matrix.  Ie. AB will have m rows and r columns.  Officially:  When finding the product AB of two matrices, the entry in (i, j) of AB is the sum of the products of the corresponding elements in row i of matrix A and column j of matrix B.

7. Say what?  When finding the product AB of two matrices, the entry in (i, j) of AB is the sum of the products of the corresponding elements in row i of matrix A and column j of matrix B.  Example: Question: Does the number of columns in A equal the number of rows in B?

8. Example 2

9. Example 3

10. Homework  Pg. 69 # 29-40 [5]