Assignment Answers. 1.7: Multiplication with Matrices.

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Assignment Answers

1.7: Multiplication with Matrices

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

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

Concept

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.

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.

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.

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.

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

Example 2 A. B. C. D.

Example 4 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.

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.

Assignment Pg #15-17 all, 23, 24, 25, 26, 35, 46, 48