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11.1: Matrix Operations [Algebra 2(Y)] ADP Content Standards: M1.a: Perform addition, subtraction, and scalar multiplication of matrices. CCSS for High School Mathematics: N.VM.6: Perform operations on matrices and use matrices in applications. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. N.VM.7: Perform operations on matrices and use matrices in applications. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. N.VM.8: Perform operations on matrices and use matrices in applications. (+) Add, subtract, and multiply matrices of appropriate dimensions. Objective: To perform matrix addition, subtraction, and scalar multiplication. Matrix A matrix is a rectangular arrangement of numbers in horizontal rows (m) and vertical columns (n)—which can be used to organize data. Each number in a matrix is called an element. Matrix: A rectangular arrangement of numbers in horizontal rows and vertical columns. (*Organizes data) Element: each number in a matrix Dimensions of a Matrix: m x n (where m = #rows, and n = #columns) Example: m = rows 10 15 A 8 12 n = columns 5 14 The dimensions are 3 x 2 Equal Matrices: have the same dimensions and their elements in corresponding positions are equal. Example 1: Compare Matrices A local bakery keeps track of their sales using a matrix. A sample is shown below. Tell whether each matrix is equal to the bakery’s matrix. Explain. Month 1 Store Store 2 1 rolls 650 540 cakes 220 200 pies 32 30 540 650 b.) a.) 650 220 32 A A 220 20(10) 9(6) 200 3(15) 30 8( 4) Adding and Subtracting Matrices In order to add or subtract matrices, you must do the following: Make sure the dimensions of each matrix are the same. If the dimensions are not the same, you cannot add or subtract. Add or subtract each corresponding element. Example 2: Add and Subtract Matrices Add or subtract, if possible. If not possible, state the reason. 2 4 3 2 a.) 0 1 4 0 6 2 4 2 2 4 b.) 5 3 1 3 4 4 7 c.) 4 3 2 3 2 1 Example 3: Solve a Matrix Equation Solve the matrix equation for x. 4x 2 3 2 15 4 5 0 4 3 9 3 Scalar Multiplication To perform scalar multiplication on a matrix, multiply the factor on the outside to each element in the matrix. Be sure to write your answers in their respective position in the original matrix. Example 4: Scalar Multiplication 3 0 a.) 4 2 1 1 4 b.) 2 0 3