Download 4-1 Matrix Properties, Adding, and Subtracting

4-1 Matrices and Data
The table shows the top scores for girls in barrel
racing at the 2004 National High School Rodeo
finals. The data can be presented in a table or a
spreadsheet as rows and columns of numbers. You
can also use a matrix to show table data.
A matrix is a rectangular array of numbers
enclosed in brackets.
Holt Algebra 2
4-1 Matrices and Data
The dimensions of a matrix are determined by its
number of rows and columns (in that order).
Matrix A has dimensions 2  3.
Each value in a matrix is called an entry of the matrix.
Holt Algebra 2
4-1 Matrices and Data
The address of an entry is its location in a matrix,
expressed by using the lower case matrix letter with
row and column number as subscripts. The score
16.206 is located in row 2 column 1, so a21 is 16.206.
Holt Algebra 2
4-1 Matrices and Data
Example 1: Displaying Data in Matrix Form
The prices for different
sandwiches are
presented at right.
6 in
9 in
Roast beef
$3.95
$5.95
Turkey
$3.75
$5.60
Tuna
$3.50
$5.25
A. Display the data in
3.95
matrix form.
P = 3.75
5.60
3.50
5.25
5.95
B. What are the dimensions of P?
P has three rows and two columns, so it is a 3  2
matrix.
Holt Algebra 2
4-1 Matrices and Data
Example 1: Displaying Data in Matrix Form
The prices for different
sandwiches are
presented at right.
6 in
9 in
Roast beef
$3.95
$5.95
Turkey
$3.75
$5.60
Tuna
$3.50
$5.25
C. What is entry p12? What does is represent?
The entry at p12, in row 1 column 2, is 5.95. It is
the price of a 9 in. roast beef sandwich.
D. What is the address of the entry 3.50?
The entry 3.50 is at p31.
Holt Algebra 2
4-1 Matrices and Data
Check It Out! Example 1
Use matrix M to
answer the
questions below.
a. What are the dimensions of M?
b. What is the entry at m32?
34
11
c. The entry 0 appears at what two addresses?
m14 and m23
Holt Algebra 2
4-1 Matrices and Data
You can add or subtract two matrices if
they have the exact same dimensions.
Simply add or subtract the corresponding
entries.
Holt Algebra 2
4-1 Matrices and Data
Example 2A: Finding Matrix Sums and Differences
Add or subtract, if possible.
W=
3 –2
1
0
,X=
4
7
2
5
1 –1
, Y=
1
4
–2 3
, Z=
2 –2 3
1
0
4
W+Y
Add each corresponding entry.
W+Y=
Holt Algebra 2
3 –2
1
0
+
1
4
–2 3
=
3+1
1 + (–2)
–2 + 4
0+3
=
4
2
–1 3
4-1 Matrices and Data
Example 2B: Finding Matrix Sums and Differences
Add or subtract, if possible.
W=
3 –2
1
0
,X=
4
7
c
a
1 –1
, Y=
1
4
–2 3
, Z=
b –2 3
1
X–Z
Subtract each corresponding entry.
X–Z=
Holt Algebra 2
4
7
c
a
1 –1
–
b –2
3
1
4
0
=
4-b
9
c-3
a-1
1
–5
0
4
4-1 Matrices and Data
Example 2C: Finding Matrix Sums and Differences
Add or subtract if possible.
4
–2
A = –3 10 , B =
2
6
4
–1 –5
3
2
8
3
,C = 0
2
–9 , D =
–5 14
B–A
B is a 2  3 matrix, and A is a 3  2 matrix.
Because B and A do not have the same
dimensions, they cannot be subtracted.
Holt Algebra 2
0
1 –3
3
0
10
4-1 Matrices and Data
You can multiply a matrix by a number, called a scalar.
To find the product of a scalar and a matrix, or the
scalar product, multiply each entry by the scalar.
Holt Algebra 2
4-1 Matrices and Data
Check It Out! Example 4b
A=
4
–2
–3 10
B=
4 –1 –5
3
2
C=
8
3
2
0 –9
D = [6 –3 8]
Evaluate 2A – 3C, if possible.
=2
4
–2
–3 10
–3
3
2
0 –9
=
=
Holt Algebra 2
2(4)
2(–2)
2(–3) 2(10)
8
–4
–6 20
+
+
–3(3) –3(2)
–3(0) –3(–9)
–9 –6
0
27
=
–1 –10
–6 47
4-1 Matrices and Data
Example 3: Business Application
Use a scalar
product to find
the prices if a
10% discount is
applied to the
prices above.
Shirt Prices
T-shirt
Sweatshirt
Small
$7.50
$15.00
Medium
$8.00
$17.50
Large
$9.00
$20.00
$10.00
$22.50
X-Large
You can multiply by 0.1 and subtract from the
original numbers.
7.5
15
8
17.5
9
20
10
22.5
Holt Algebra 2
7.5
– 0.1 8
15
17.5
9
20
10
22.5
=
6.75
13.50
7.5 15
7.20
15.75
8
17.5
–
8.10
18.00
9
20
9.00
20.25
10 22.5
0.75
1.5
0.8
1.75
0.9
2
1
2.25
4-1 Matrices and Data
Holt Algebra 2
4-1 Matrices and Data
Homework:
Page 251
#’s 18-22, 24-27, 29
Holt Algebra 2