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The Algebra of Matrices Matrix: An array of numbers. Columns 3 2 5 A 2 3 1 4 0 Matrix Name (Capital Letter) Matrix Size (row x column) Rows Elements: arc a22 = 4 Addition/Subtraction of Matrices: • Two matrices can only be added/subtracted if they have the same dimensions. 3+5=8 3 2 5 A 2 3 1 4 0 5 4 1 B 2 3 3 0 2 Add the corresponding elements! a811 a12 A B a21 a22 a13 a23 Subtract the corresponding elements! 3 - 5 = -2 3 2 5 A 2 3 1 4 0 -2 A B 5 4 1 B 2 3 3 0 2 Scalar Multiplication: Multiply each element in the matrix by the real number. (2x3=6) 3 2 5 A 2 3 1 4 0 6 2A Try This: 2 1 A 4 0 3 5 4 3 B 1 0 1 2 2A - B = 8 5 7 0 5 8 Multiplication of Matrices: • Two matrices can only be multiplied if the number of columns of the first matrix equals the number of rows in the second matrix. A23 B32 AB22 = Product Dimensions •The dimensions of the product matrix will then be the number of rows from the first matrix by the number of columns in the second. 2 0 3 A 23 B33 1 4 2 Example: 2 1 1 3 4 1 0 3 3 ab11 = Sum of products of elements from row 1 of matrix A with the corresponding elements from column 1 of matrix B. ab11 = (-2 x 2) + (0 x 3) + (3 x 0) = -4 AB23 a- 4 a 11 a12 21 a22 a a 13 23 Example: 2 0 3 A 23 1 4 2 Find BA: B33 2 1 1 3 4 1 0 3 3 Example: Find A2: 2 3 A 4 1 Playing The Stock Market: Three investors Kelsey, Nicole, and Linda each own a certain number of shares of four stocks - McDonalds, Coke, Walmart, and AT&T. Number of Shares of Stock McDonalds Coke Walmart AT&T Kelsey 50 100 30 25 30 Nicole 100 150 10 Linda 100 50 40 100 Current Value of Each Share McDonalds Coke Walmart AT&T $ 20.37 $ 16.21 $ 90.80 $ 42.75 Find each students’ current cash-in value for their stocks. Kelsey (50 20.37) (100 16.21) (30 90.80) (25 42.75) $ 6,432.25 Nicole (100 20.37) (150 16.21) (10 90.80) (30 42.75) $ 6,659 Linda (100 20.37) (50 16.21) (40 90.80) (100 42.75) $ 10,754.50 Kelsey Nicole Linda $6,432.25 $6,659.00 $10,754.50