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Example 1 Dimensions of Matrix Products A. Determine whether the product of A 3×4 and B 4×2 is defined. If so, state the dimensions of the product. Answer: The inner dimensions are equal so the matrix product is defined. The dimensions of the product are 3 × 2. A●B=AB 3 × 44 × 23 × 2

Example 1 Dimensions of Matrix Products B. Determine whether the product of A 3×2 and B 4×3 is defined. If so, state the dimensions of the product. Answer: The inner dimensions are not equal, so the matrix product is not defined. A●BA●B 3 × 24 × 3

Example 1 A.3 × 3 B.2 × 2 C.3 × 2 D.The matrix product is not defined. A. Determine whether the matrix product is defined. If so, what are the dimensions of the product? A 3×2 and B 2×3

Example 1 A.2 × 3 B.3 × 2 C.2 × 2 D.The matrix product is not defined. B. Determine whether the matrix product is defined. If so, what are the dimensions of the product? A 2×3 and B 2×3

Concept

Example 2 Multiply Square Matrices

Example 2 Multiply Square Matrices Step 1Multiply the numbers in the first row of R by the numbers in the first column of S, add the products, and put the result in the first row, first column of RS.

Example 2 Multiply Square Matrices Step 2Multiply the numbers in the first row of R by the numbers in the second column of S, add the products, and put the result in the first row, second column of RS.

Example 2 Multiply Square Matrices Step 3Multiply the numbers in the second row of R by the numbers in the first column of S, add the products, and put the result in the second row, first column of RS.

Example 2 Multiply Square Matrices Step 4Multiply the numbers in the second row of R by the numbers in the second column of S, add the products, and put the result in the second row, second column of RS.

Example 2 Multiply Square Matrices Step 5Simplify the product matrix. Answer:

Example 2 A. B. C. D.

Example 3 Multiply Matrices CHESS Three teams competed in the final round of the Chess Club’s championships. For each win, a team was awarded 3 points and for each draw a team received 1 point. Which team won the tournament? Understand The final scores can be found by multiplying the wins and draws by the points for each.

Example 3 Multiply Matrices PlanWrite the results from the championship and the points in matrix form. Set up the matrices so that the number of rows in the points matrix equals the number of columns in the results matrix. ResultsPoints

Example 3 Multiply Matrices SolveMultiply the matrices. Write an equation. Multiply columns by rows.

Example 3 Multiply Matrices Simplify. The labels for the product matrix are shown below. Blue Red Green Total Points

Example 3 Multiply Matrices Answer: The red team won the championship with a total of 21 points. CheckR is a 3 × 2 matrix and P is a 2 × 1 matrix. Their product should be a 3 × 1 matrix.

Example 3 A.Warton B.Bryant C.Chris D.none of the above BASKETBALL In Thursday night’s basketball game, three of the players made the points listed below in the chart. They scored 1 point for the free-throws, 2 points for the 2-point shots, and 3 points for the 3-points shots. Who scored the most points?

Example 4 Test of the Commutative Property Substitution Multiply columns by rows. Simplify. A. Find KL if K

Example 4 Test of the Commutative Property Answer:

Example 4 Test of the Commutative Property Substitution Multiply columns by rows. B. Find LK if K

Example 4 Test of the Commutative Property Answer: Simplify.

Example 4 A. B. C. D.

Example 4 A. B. C. D.

Example 5 Test of the Distributive Property Substitution Add corresponding elements. A.

Example 5 Test of the Distributive Property Multiply columns by rows. Answer:

Example 5 Test of the Distributive Property Multiply columns by rows. Substitution

Example 5 Test of the Distributive Property Simplify. Answer: Add corresponding elements.

Example 5 A.B. C.D.

Example 5 A.B. C.D.

Concept

Homework: Section 6 (pg 184): 15 – 47 odd, 34, 44, & 46(25 problems) 51 – 54 all(4 problems)

End of the Lesson