Lesson 4.3Multiplying Matrices Matrix Multiplication Property [A][B] is possible iff the number of columns in [A] match the rows in [B]. Possible Result n x b

Example 1Multiplication Property Determine whether the [A][B] is possible, if so, give the dimensions of the resulting matrix. a)b) c)

To multiply: Multiply each row by each column 1.1 st row times column (first element of row times first element of column plus second element of row times second element of column) = = == 2. 2nd row times column (first element of row times first element of column plus second element of row times second element of column)

a) b) Example 2Multiplying Matrices Determine whether the [A][B] is possible, if so multiply them Calculator Free.

To multiply: Multiply each row by each column 1. 1st row times 1st column (first element of row times first element of column plus second element of row times second element of column) = = = = = = = = 2. 1st row times 2nd column 3. 2nd row times 1st column 4. 2nd row times 2nd column

Example 2Multiplying Matrices c) d)

Example 3Multiplying Matrices Determine whether the [A][B] is possible, if so multiply them. Use a Calculator. a) b)

Example 4Application Problems a)The senior class play was performed on three different evenings. The attendance for each night is shown below. Adult tickets sold for $3.50 and students for $2.50. Use matrix multiplication to determine how much money was taken in each night. NightAdultsStudents Thursday Friday Saturday Thursday Friday Saturday

Example 4Application Problems b)Jim wrote 3 comic books. He plans to sell them for $1.50, $2.25, and $3.15 respectively. The table below reflects the sales for the first 3 days. Use matrix multiplication to find the daily totals. DayComic #1Comic #2Comic #3 Monday Tuesday Wednesday Monday Tuesday Wednesday