Chapter 8 Lesson 8 2 Operations With Matrices

Chapter 8: Lesson 8. 2 Operations With Matrices 2 matrices are said to be equal if the size or “order” of the 2 matrices is the same AND all corresponding elements of the 2 matrices are the same. 2 matrices can only be added if they are of equal order. If you are asked to add or subtract matrices that are not of equal order, simply write “impossible. ” #12 Find A + B, A- B, 3 A and 3 A – 2 B if

Definition of Matrix Multiplication • 2 matrices can multiplied together only if the number of columns of the 1 st matrix is equal to the number of rows of the 2 nd matrix. The size or order of the resulting matrix multiplication will be the rows of the first by the columns of the 2 nd. In other words, a (3 x 3) (3 x 1) = (3 x 1) • Note that A B ≠ B A (Matrix Multiplication is NOT Commutative) • Be my guest to try and figure out matrix multiplication from page 556, I’d prefer to teach it just through examples and understanding the pattern based on that.

#36 Find AB if

#35 Find AB if

Identity Matrix An Identity Matrix has all 1’s on the main diagonal and 0’s everywhere else. See page 558.

#74 The number of calories burned by individuals of different body weights while performing different types of exercises for a one-hour time period are represented by A. Calories burned 130 -lb 155 -lb person Basketball Jumping Rope Weight Lifting a) A 130 -pound person and a 155 -pound person played basketball for 2 hours, jumped rope for 15 minutes, and lifted weights for 30 minutes. Make matrix B that organizes the times spent exercising. b) Compute BA and interpret the results