Assignment Answers 1 7 Multiplication with Matrices Dimensions

Dimensions of Matrix Products A. Determine whether the product of A 3× 4 and

Dimensions of Matrix Products B. Determine whether the product of A 3× 2 and

Example 1 A. Determine whether the matrix product is defined. If so, what are

Multiply Square Matrices Step 1 Multiply the numbers in the first row of R

Multiply Square Matrices Step 2 Multiply the numbers in the first row of R

Multiply Square Matrices Step 3 Multiply the numbers in the second row of R

Multiply Square Matrices Step 4 Multiply the numbers in the second row of R

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

Example 4 Multiply Matrices CHESS Three teams competed in the final round of the

Multiply Matrices Plan Write the results from the championship and the points in matrix

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

Example 3 Multiply Matrices Simplify. The labels for the product matrix are shown below.

Example 3 Multiply Matrices Answer: The red team won the championship with a total

Assignment Pg. 184 -185 #15 -17 all, 23, 24, 25, 26, 35, 46, 48

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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. = 3× 4 A AB 4× 2 ● B 3× 2 Answer: The inner dimensions are equal so the matrix product is defined. The dimensions of the product are 3 × 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. A 3× 2 ● B 4× 3 Answer: The inner dimensions are not equal, so the matrix product is not defined.

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

Concept

Multiply Square Matrices

Multiply Square Matrices Step 1 Multiply 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 2 Multiply 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 3 Multiply 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 4 Multiply 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 5 Answer: Simplify the product matrix.

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 Plan Write 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. Results Points

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

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

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

Assignment Pg. 184 -185 #15 -17 all, 23, 24, 25, 26, 35, 46, 48