holt algebra 2 4-1 matrices and data the table shows the top scores for girls in barrel racing at...
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Holt Algebra 2
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
The prices for different sandwiches are presented at right.
Example 1: Displaying Data in Matrix Form6 in 9 in
Roast beef $3.95 $5.95
Turkey $3.75 $5.60
Tuna $3.50 $5.25
A. Display the data in matrix form. P =
3.95 5.95
3.75 5.60
3.50 5.25
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
C. What is entry p12? What does is represent?
D. What is the address of the entry 3.50?
The entry at p12, in row 1 column 2, is 5.95. It is the price of a 9 in. roast beef sandwich.
The entry 3.50 is at p31.
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
Holt Algebra 2
4-1 Matrices and Data
Use matrix M to answer the questions below.
Check It Out! Example 1
a. What are the dimensions of M? 3 4
11
m14 and m23
b. What is the entry at m32?
c. The entry 0 appears at what two addresses?
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
Add or subtract, if possible.
Example 2A: Finding Matrix Sums and Differences
W + Y
Add each corresponding entry.
W = , 3 –2
1 0Y = ,
1 4
–2 3X = ,
4 7 2
5 1 –1Z =
2 –2 3
1 0 4
W + Y =
3 –2
1 0+
1 4
–2 3=
3 + 1 –2 + 4
1 + (–2) 0 + 3
4 2
–1 3=
Holt Algebra 2
4-1 Matrices and Data
X – Z
Subtract each corresponding entry.
Example 2B: Finding Matrix Sums and Differences
W = , 3 –2
1 0Y = ,
1 4
–2 3X = ,
4 7 c
a 1 –1Z =
b –2 3
1 0 4
Add or subtract, if possible.
X – Z =4 7 c
a 1 –1
b –2 3
1 0 4–
4-b 9 c-3
a-1 1 –5 =
Holt Algebra 2
4-1 Matrices and Data
B – A
Add or subtract if possible.
A = ,
4 –2
–3 10
2 6
B = , 4 –1 –5
3 2 8C = ,
3 2
0 –9
–5 14
D = 0 1 –3
3 0 10
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.
Example 2C: Finding Matrix Sums and Differences
Holt Algebra 2
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
D = [6 –3 8]A =
4 –2
–3 10C =
3 2
0 –9 B =
4 –1 –5
3 2 8
Evaluate 2A – 3C, if possible.
4 –2
–3 10= 2 – 3
3 2
0 –9
2(4) 2(–2)
2(–3) 2(10)= +
–3(3) –3(2)
–3(0) –3(–9)
8 –4
–6 20= +
–9 –6
0 27 =
–1 –10
–6 47
Holt Algebra 2
4-1 Matrices and Data
Example 3: Business Application
Shirt Prices
T-shirt Sweatshirt
Small $7.50 $15.00
Medium $8.00 $17.50
Large $9.00 $20.00
X-Large $10.00 $22.50
Use a scalar product to find the prices if a 10% discount is applied to the prices above.
You can multiply by 0.1 and subtract from the original numbers.
7.5 15
8 17.5
9 20
10 22.5
7.5 15
8 17.5
9 20
10 22.5
– 0.1 =
7.5 15
8 17.5
9 20
10 22.5
0.75 1.5
0.8 1.75
0.9 2
1 2.25
–
6.75 13.50
7.20 15.75
8.10 18.00
9.00 20.25
Holt Algebra 2
4-1 Matrices and Data
Holt Algebra 2
4-1 Matrices and Data
Homework: Page 251#’s 18-22, 24-27, 29