4.1 Using Matrices to Represent Data Objectives: Represent mathematical and real-world data in a matrix. Find sums and differences of matrices and the scalar product of a number and a matrix Standard: 2.8.11.I. Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication, and scalar multiplication.

The table below shows business activity for one month in a home-improvement store. The table shows stock (inventory on June 1st), sales (during June), and receipt of new goods (deliveries in June). Sales (June) Inventory (June 1st) Deliveries (June) Small Large Picnic Table 8 10 7 9 15 20 BQ grills 12 18 24

You can represent the inventory data in a MATRIX. Small Large Picnic Table 8 10 BQ grills 15 12

* A _______________ (plural - _____________) is a rectangular array of numbers enclosed in a single set of brackets. * The _____________ of a matrix are the number of horizontal rows and the number of vertical rows it has. If a matrix has 2 rows and 3 columns, its dimensions are __________, read as “ __ .” The inventory matrix above, M, is a matrix with dimensions of _______________. * Each number in the matrix is called an ______________, or element.

Ex 1. Represent the June sales data in matrix S Ex 1. Represent the June sales data in matrix S. Interpret the entry at S12. Ex 2. Represent the June delivery data in matrix D. Interpret the entry at D21.

* 2 matrices are equal if they’ve the same _____________ & if corresponding entries are ___________________.

* Ex. 2 Solve for x and y. 4x + 5 9 15 21 9 15 = 7 -2y + 3 -1 7 y – 12 -1

To find the sum (or difference) of matrices A and B with the same dimensions, find the sums (or differences) of corresponding entries in A and B.

and * Ex. 2 Let

* To multiply a matrix, A, by a real number, k, write a matrix whose entries are k times each of the entries in matrix A. This operation is called _____________________________

* Let Find -3A.

is the additive inverse of A. * When k = -1, the scalar product kA is -1A, or simply –A, and is called the _____________ or opposite, of matrix A. For example, then –A = ___?____ is the additive inverse of A. * Let

Writing Activities 1). If A represents a matrix, explain what -5A represents. 2). If M is 4 X 5 matrix, explain what the numbers 4 and 5 represent.