Matrix Multiplication

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Matrix Multiplication Example 1 Original author: Jeffrey Bivin, Lake Zurich High School

Matrix Multiplication 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X Row by Column Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 3 x 5 + 2 x 0 + 5 x 2 = 25 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 3 x 5 + 2 x 0 + 5 x 2 = 25 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 3 x 5 + 2 x 0 + 5 x 2 = 25 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 = A(1,1) Original author: Jeffrey Bivin, Lake Zurich High School

3 x (-1) + 2 x 3 + 5 x 7 = 38 X Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X 3 x (-1) + 2 x 3 + 5 x 7 = 38 Original author: Jeffrey Bivin, Lake Zurich High School

3 x (-1) + 2 x 3 + 5 x 7 = 38 X Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X 3 x (-1) + 2 x 3 + 5 x 7 = 38 Original author: Jeffrey Bivin, Lake Zurich High School

3 x (-1) + 2 x 3 + 5 x 7 = 38 X Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X 3 x (-1) + 2 x 3 + 5 x 7 = 38 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 = A(1,2) Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 3 x 2 + 2 x 7 + 5 x 4 = 40 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 3 x 2 + 2 x 7 + 5 x 4 = 40 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 3 x 2 + 2 x 7 + 5 x 4 = 40 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 = A(1,3) Original author: Jeffrey Bivin, Lake Zurich High School

-2 x 5 + 0 x 0 + 1 x 2 = -8 X Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 1 4 6 9 5 -1 2 3 7 4 X -2 x 5 + 0 x 0 + 1 x 2 = -8 Original author: Jeffrey Bivin, Lake Zurich High School

-2 x 5 + 0 x 0 + 1 x 2 = -8 X Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 1 4 6 9 5 -1 2 3 7 4 X -2 x 5 + 0 x 0 + 1 x 2 = -8 Original author: Jeffrey Bivin, Lake Zurich High School

-2 x 5 + 0 x 0 + 1 x 2 = -8 X Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 1 4 6 9 5 -1 2 3 7 4 X -2 x 5 + 0 x 0 + 1 x 2 = -8 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 = A(2,1) Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X Original author: Jeffrey Bivin, Lake Zurich High School

-2 x (-1) + 0 x 3 + 1 x 7 = 9 X Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X -2 x (-1) + 0 x 3 + 1 x 7 = 9 Original author: Jeffrey Bivin, Lake Zurich High School

-2 x (-1) + 0 x 3 + 1 x 7 = 9 X Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X -2 x (-1) + 0 x 3 + 1 x 7 = 9 Original author: Jeffrey Bivin, Lake Zurich High School

-2 x (-1) + 0 x 3 + 1 x 7 = 9 X Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X -2 x (-1) + 0 x 3 + 1 x 7 = 9 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 = A(2,2) Original author: Jeffrey Bivin, Lake Zurich High School

-2 x 2 + 0 x 7 + 1 x 4 = 0 X Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 1 4 6 9 5 -1 2 3 7 4 X -2 x 2 + 0 x 7 + 1 x 4 = 0 Original author: Jeffrey Bivin, Lake Zurich High School

-2 x 2 + 0 x 7 + 1 x 4 = 0 X Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 1 4 6 9 5 -1 2 3 7 4 X -2 x 2 + 0 x 7 + 1 x 4 = 0 Original author: Jeffrey Bivin, Lake Zurich High School

-2 x 2 + 0 x 7 + 1 x 4 = 0 X Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 1 4 6 9 5 -1 2 3 7 4 X -2 x 2 + 0 x 7 + 1 x 4 = 0 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 = A(2,3) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 4 x 5 + 6 x 0 + 9 x 2 = 38 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 4 x 5 + 6 x 0 + 9 x 2 = 38 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 4 x 5 + 6 x 0 + 9 x 2 = 38 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 = A(3,1) Original author: Jeffrey Bivin, Lake Zurich High School

4 x (-1) + 6 x 3 + 9 x 7 = 77 X Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X 4 x (-1) + 6 x 3 + 9 x 7 = 77 Original author: Jeffrey Bivin, Lake Zurich High School

4 x (-1) + 6 x 3 + 9 x 7 = 77 X Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X 4 x (-1) + 6 x 3 + 9 x 7 = 77 Original author: Jeffrey Bivin, Lake Zurich High School

4 x (-1) + 6 x 3 + 9 x 7 = 77 X Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -1 1 4 6 9 5 -1 2 3 7 4 X 4 x (-1) + 6 x 3 + 9 x 7 = 77 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 = A(3,2) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 4 x 2 + 6 x 7 + 9 x 4 = 86 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 4 x 2 + 6 x 7 + 9 x 4 = 86 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 4 x 2 + 6 x 7 + 9 x 4 = 86 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86 A(3,3) Original author: Jeffrey Bivin, Lake Zurich High School

Matrix Multiplication 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86 = Original author: Jeffrey Bivin, Lake Zurich High School

Matrix Multiplication Example 2 Original author: Jeffrey Bivin, Lake Zurich High School

Matrix Multiplication 3 5 -2 1 4 9 5 2 3 4 X Row by Column Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 3 x 5 + 5 x 3 = 30 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 3 x 5 + 5 x 3 = 30 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 = A(1,1) Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 3 x 2 + 5 x 4 = 26 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 3 x 2 + 5 x 4 = 26 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 = A(1,2) Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X -2 x 5 + 1 x 3 = -7 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X -2 x 5 + 1 x 3 = -7 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,1) Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X -2 x 2 + 1 x 4 = 0 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X -2 x 2 + 1 x 4 = 0 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,2) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 4 x 5 + 9 x 3 = 47 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 4 x 5 + 9 x 3 = 47 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 = A(3,1) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 4 x 2 + 9 x 4 = 44 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 4 x 2 + 9 x 4 = 44 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 = A(3,2) Original author: Jeffrey Bivin, Lake Zurich High School

Matrix Multiplication 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 = Original author: Jeffrey Bivin, Lake Zurich High School

Matrix Multiplication Example 3 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 2 + 3 x 4 = 22 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 2 + 3 x 4 = 22 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X 22 = A(1,1) Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 2 + 3 x 4 = 22 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 0 + 3 x 5 = 15 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 = A(1,2) Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 1 + 3 x 5 = 15 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 1 + 3 x 2 = 11 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 = A(1,3) Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 3 + 3 x 6 = 33 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X 5 x 3 + 3 x 6 = 33 Original author: Jeffrey Bivin, Lake Zurich High School

Row 1 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 = A(1,4) Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 2 + 4 x 4 = 12 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 2 + 4 x 4 = 12 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 = A(2,1) Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 0 + 4 x 5 = 20 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 0 + 4 x 5 = 20 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 = A(2,2) Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 1 + 4 x 2 = 6 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 1 + 4 x 2 = 6 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 6 = A(2,3) Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 3 + 4 x 6 = 18 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X -2 x 3 + 4 x 6 = 18 Original author: Jeffrey Bivin, Lake Zurich High School

Row 2 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 6 18 = A(2,4) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 2 + 0 x 4 = -2 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 2 + 0 x 4 = -2 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 1 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 6 18 -2 = A(3,1) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 0 + 0 x 5 = 0 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 0 + 0 x 5 = 0 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 2 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 6 18 -2 = A(3,2) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 1 + 0 x 2 = -1 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 1 + 0 x 2 = -1 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 3 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 6 18 -2 -1 = A(3,3) Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 3 + 0 x 6 = -3 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X -1 x 3 + 0 x 6 = -3 Original author: Jeffrey Bivin, Lake Zurich High School

Row 3 x Column 4 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 6 18 -2 -1 -3 = A(3,4) Original author: Jeffrey Bivin, Lake Zurich High School

Matrix Multiplication 5 3 -2 4 -1 2 1 3 4 5 6 X 22 15 11 33 12 20 6 18 -2 -1 -3 = Original author: Jeffrey Bivin, Lake Zurich High School