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Matrix Multiplication

Matrix Multiplication. Matrix multiplication involves both multiplication and addition. The process can be demonstrated using football scores. Suppose a team scores 5 touchdowns, 4 extra points, and 2 field goals. To find the total points scored multiply:.

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Matrix Multiplication

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  1. Matrix Multiplication

  2. Matrix multiplication involves both multiplication and addition. The process can be demonstrated using football scores. Suppose a team scores 5 touchdowns, 4 extra points, and 2 field goals. To find the total points scored multiply: (5)(6) + (4)(1) + (2)(3) = 30 + 4 + 6 = 40 since TD’s are worth 6 points, extra points are worth 1 point, and field goals are worth 3 points.

  3. To model this with matrix multiplication, represent the number of TD’s, extra points, and field goals in a 1 x 3 matrix. Represent the point values of each in a 3 x 1 matrix. Notice that the product of a 1 x 3 matrix and a 3 x 1 matrix is a 1 x 1 matrix.

  4. To determine if it is possible to multiply matrices it is necessary to look at their dimensions. Matrices may be multiplied only if the inner dimensions are the same. Outer dimensions 1 x 33 x 1 Inner dimensions The dimensions of the product matrix are the same as the outer dimensions of the factors.

  5. Is it possible to find the product AB? Write the product with the matrix dimensions: This product is not possible because the inner dimensions are different.

  6. Is it possible to find the product BA? Write the product with the matrix dimensions: This product is possible because the inner dimensions are the same. The product will be a 2 x 3 matrix.

  7. Matrix Multiplication If matrix A has dimensions m x n and matrix B has dimensions n x r, then the product AB has dimensions m x r. Find the entry in row i and column j of AB by finding the sum of the products of the corresponding entries in row i of A and column j of B.

  8. Find HG, if it exists.

  9. Write the product matrix with the row/column designation of each entry. Notice that this is the product of row 1 and column 1.

  10. Notice that this is the product of row 1 and column 2.

  11. Notice that this is the product of row 2 and column 1.

  12. Notice that this is the product of row 2 and column 2.

  13. Therefore, the product HG = Is the product GH the same thing?

  14. Find GH, if it exists.

  15. Write the product matrix with the row/column designation of each entry. Notice that this is the product of row 1 and column 1.

  16. Notice that this is the product of row 1 and column 2.

  17. Notice that this is the product of row 2 and column 1.

  18. Notice that this is the product of row 2 and column 2.

  19. Therefore, the product GH = Is matrix multiplication commutative? Even though both HG and GH exist they are not equal. Therefore, matrix multiplication is not commutative.

  20. Find RW, if it exists.

  21. Find WR, if it exists. WR does not exist.

  22. Matrix Multiplication - Application Karl and Kayla are making two snack mixes by mixing dried fruit and nuts. The amounts of protein, carbohydrates, and fat, in grams per serving, for the dried fruit and nuts are given in Table 1. The number of servings of dried fruit and nuts in each is given in Table 2.

  23. Table 1 Table 2

  24. Represent the information from Table 1 in a matrix called N. Represent the information from Table 2 in a matrix called G.

  25. Find the product NG, and determine which mix has more protein and which mix has less fat. The camp mix has more protein, 69 grams. The sport mix has less fat, 108 grams. Sport Mix Camp Mix Protein Carbohydrate Fat

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