Transcript 4.1 Using Matrices to Represent Data

4.1 Using Matrices to
Represent Data
Objectives: Represent mathematical and realworld 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
Small
Large
Small
Large
Picnic
Table
8
10
7
9
15
20
BQ
grills
15
12
15
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. 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.
* Ex. 2 Let
and
* 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.
* When k = -1, the scalar product kA is -1A, or
simply –A, and is called the _____________
or opposite, of matrix A. For example,
* Let
then –A = ___?____
is the additive inverse
of A.
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.