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4-3: Matrix Multiplication

Essential Question: Unfortunately, no one can be told how to calculate a matrix. You have to do it yourself. 4-3: Matrix Multiplication. 4-3: Multiplying Matrices. Two matrices can be multiplied together if the number of columns from A is equal to the number of rows of B.

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4-3: Matrix Multiplication

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  1. Essential Question: Unfortunately, no one can be told how to calculate a matrix. You have to do it yourself. 4-3: Matrix Multiplication

  2. 4-3: Multiplying Matrices • Two matrices can be multiplied together if the number of columns from A is equal to the number of rows of B. • The resulting matrix will have the dimensions: (rows of A) x (columns of B) Resulting matrix will be: 3 x 4 2 x 4 3 x 2 must match

  3. 4-3: Multiplying Matrices • Determine whether each product is defined or undefined. If it is defined, find the dimensions of the product. • FJ: • JF: • HJ: • JH: (2 x 2)(1 x 2) undefined (1 x 2)(2 x 2) defined, 1 x 2 matrix (2 x 1)(1 x 2) defined, 2 x 2 matrix (1 x 2)(2 x 1) defined, 1 x 1 matrix

  4. 4-3: Multiplying Matrices • To perform matrix multiplication, multiply the elements of each row of the first matrix by each column of the second matrix. Add the products. -1 -3 0 3 3 -3 = -29 9 5 0 3 -4 1st row x 1st column: (-1)(-3) + (0)(5) = 3 + 0 = 3 1st row x 2nd column: (-1)(3) + (0)(0) = -3 + 0 = -3 2nd row x 1st column: (3)(-3) + (-4)(5) = -9 – 20 = -29 2nd row x 2nd column: (3)(3) + (-4)(0) = 9 + 0 = 9

  5. 4-3: Multiplying Matrices • Your Turn #1: Find the product -3 -1 3 0 12 -12 = -5 0 3 -4 5 0 1st row x 1st column: (-3)(-1) + (3)(3) = 3 + 9 = 12 1st row x 2nd column: (-3)(0) + (3)(-4) = 0 – 12 = -12 2nd row x 1st column: (5)(-1) + (0)(3) = -5 + 0 = -5 2nd row x 2nd column: (5)(0) + (0)(-4) = 0 + 0 = 0

  6. 4-3: Multiplying Matrices • Your Turn #2: Find the product • Can they be multiplied? 12 10 3 105 = -5 Yes, (1 x 2)(2 x 1) gives a 1 x 1 matrix 1st row x 1st column: (12)(10) + (3)(-5) = 120 – 15 = 105

  7. 4-3: Multiplying Matrices • Your Turn #3: Find the product • Can they be multiplied? 12 3 10 -5 0 0 No, (2 x 1)(2 x 2) is undefined

  8. 4-3: Multiplying Matrices • Assignment • Page 187, 11 – 16 & 20 – 25 (all problems)

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