4.1 Using Matrices to 4.1 Using Matrices to Represent DataRepresent Data

ObjectivesObjectives: Represent mathematical and real-: Represent mathematical and real-world data in a matrix. Find sums and world data in a matrix. Find sums and

differences of matrices and the scalar product of differences of matrices and the scalar product of a number and a matrixa number and a matrix

StandardStandard: 2.8.11.I. Use matrices to organize and : 2.8.11.I. Use matrices to organize and manipulate data, including matrix addition, manipulate data, including matrix addition,

subtraction, multiplication, and scalar subtraction, multiplication, and scalar multiplication.multiplication.

The table below shows business activity for one The table below shows business activity for one month in a home-improvement store. The table shows month in a home-improvement store. The table shows stock (inventory on June 1st), sales (during June), and stock (inventory on June 1st), sales (during June), and

receipt of new goods (deliveries in June).receipt of new goods (deliveries in June).

SmallSmall LargeLarge SmallSmall LargeLarge SmallSmall LargeLarge

PicnicPicnic

TableTable 88 1010 77 99 1515 2020

BQBQ

grillsgrills1515 1212 1515 1212 1818 2424

Inventory (June 1st)

Sales(June)

Deliveries

(June)

You can represent the inventory You can represent the inventory data in a data in a MATRIX.MATRIX.

SmallSmall LargeLarge

PicnicPicnic

TableTable

88 1010

BQBQ

grillsgrills

1515 1212

** A _______________ (plural - A _______________ (plural - _____________) is a rectangular array of _____________) is a rectangular array of numbers enclosed in a single set of numbers enclosed in a single set of brackets.brackets.

* * The _____________ of a matrix are the The _____________ of a matrix are the number of horizontal rows and the number number of horizontal rows and the number of vertical rows it has. If a matrix has 2 of vertical rows it has. If a matrix has 2 rows and 3 columns, its dimensions are rows and 3 columns, its dimensions are __________, read as “__________, read as “ __ . __ .” The ” The inventory matrix above, inventory matrix above, MM, is a matrix with , is a matrix with dimensions of _______________.dimensions of _______________.

* * Each number in the matrix is called an Each number in the matrix is called an ______________, or element.______________, or element.

Ex 1. Represent the June sales data in matrix Ex 1. Represent the June sales data in matrix SS. Interpret the entry at . Interpret the entry at SS1212..

Ex 2. Represent the June delivery data in Ex 2. Represent the June delivery data in matrix matrix D. D. Interpret the entry at Interpret the entry at DD2121..

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

___________________.___________________.

44xx + 5 9 15 21 9 15 + 5 9 15 21 9 15 == 7 -27 -2yy + 3 -1 7 + 3 -1 7 yy – 12 -1 – 12 -1

* Ex. 2 Solve for x and y.

To find the sum (or difference) of matrices To find the sum (or difference) of matrices AA and and BB with the with the same dimensions, find the sums (or differences) of same dimensions, find the sums (or differences) of

correspondingcorresponding entries in entries in AA and and BB..

* Ex. 2 Let and

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

__________________________________________________________

* Let Find -3A.

* * When When kk = -1, the scalar product = -1, the scalar product kAkA is -1 is -1AA, or , or simply –simply –AA, and is called the _____________, and is called the _____________

or opposite, of matrix or opposite, of matrix AA. For example,. For example,

* Letthen –A = ___?____ is the additive inverse of A.

Writing ActivitiesWriting Activities

1). If 1). If A A represents a matrix, explain what represents a matrix, explain what -5-5AA represents. represents.

2). If2). If M M is 4 is 4 XX 5 matrix, explain what the 5 matrix, explain what the numbers 4 and 5 represent.numbers 4 and 5 represent.