LEQ: WHAT IS THE PROCESS USED TO MULTIPLY MATRICES? Matrix Multiplication Sec. 4-3

Matrix Multiplication The product of two matrices exists only when the number of columns of the first matrix equals the number of rows of the second matrix For example: equal dimensions of product

Matrix Multiplication (continued) The product of two matrices is the matrix whose element in row m and column n is the product of row m of the first matrix and column n of the second matrix. Row by Column multiplication

For example  Product of row 1 of the first matrix and column 1 of the second matrix is 8 * * 0 = 8. This is put in row 1 column 1 of the answer.  Product of row 1 column 2 is 8 * * 4 = 16. This is put in row 1 column 2 of the answer.  Product of row 1 column 3 is 8 * * 2 = 36. This is put in row 1 column 3 of the answer.  Row 2 column 1 is 4 * * 0 = 4  Row 2 column 2 is 4 * * 4 = 16  Row 2 column 3 is 4 * * 2 = 22

Matrices in real life There are several choices for arranging your data. When making your choice, remember the number of columns of the first matrix must equal the number of rows of the second matrix. It is helpful to consider the units involved  The headings of the column of the left matrix must match the headings of the rows of the right matrix.

For example Both Joe and Bob tutor students in math. They each charge $10 per hour for one person and $25 an hour for a small group. Every week Joe tutors 3 people individually an hour each and works with 2 small groups for an hour each. Bob tutors 5 people individually for an hour each and works with one small group for an hour. Use matrix multiplication to find the total amount earned by each tutor. Matrix A: Ind. Gr. Joe Bob Matrix B: Earn Ind. Gr. A*B = Earn Joe Bob Joe earned $80 and Bob earned $75.

Matrices on the graphing calculator Key strokes to matrix menu: 2 nd, x -1 To enter matrices slide over to EDIT and select a matrix  Enter # of rows and # of columns  Enter each element…make sure to press enter after each one  To enter a different matrix, 2 nd, x -1, EDIT, chose a different matrix Must quit (2 nd, MODE) after entering matrices To perform operations with matrices (add, subtract, scalar multiply, multiply…), 2 nd, x -1, NAMES and chose the matrix desired.  Puts the matrix in the “working screen”  Use the add, subtract, and multiply buttons to indicate desired operation.  Go back into the matrix menu and retrieve the other matrix needed under NAMES.

For example Use a graphing calculator to find:  A * B  -3 * B

Homework Pgs #1-7, 10-16, 20-22