Download 11.1: Matrix Operations - Algebra 1 and Algebra 2

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 
