Holt Algebra 2 4-1 Matrices and Data 4-1 Matrices and Data Holt Algebra 2 Warm Up Warm Up Lesson...
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Transcript of Holt Algebra 2 4-1 Matrices and Data 4-1 Matrices and Data Holt Algebra 2 Warm Up Warm Up Lesson...
Holt Algebra 2
4-1 Matrices and Data4-1 Matrices and Data
Holt Algebra 2
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt Algebra 2
4-1 Matrices and Data
Warm UpDistribute.
1. 3(2x + y + 3z)
2. –1(x – y + 2)
6x + 3y + 9z
–x + y – 2
Holt Algebra 2
4-1 Matrices and Data
Use matrices to display mathematical and real-world data.
Find sums, differences, and scalar products of matrices.
Objectives
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
Matrix A has two rows and three columns. A matrix with m rows and n columns has dimensions m n, read “m by n,” and is called an m n 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
You can add or subtract two matrices only if they have the same dimensions.
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 2
5 1 –1Z =
2 –2 3
1 0 4
Add or subtract, if possible.
X – Z =4 7 2
5 1 –1
2 –2 3
1 0 4–
2 9 –1
4 1 –5 =
Holt Algebra 2
4-1 Matrices and Data
Example 4A: Simplifying Matrix Expressions
Evaluate 3P — Q, if possible.
P =
3 –2
1 0
2 –1
Q=4 7 2
5 1 –1R =
1 4
–2 3
0 4
P and Q do not have the same dimensions; they cannot be subtracted after the scalar products are found.
Holt Algebra 2
4-1 Matrices and Data
Example 4B: Simplifying Matrix Expressions
Evaluate 3R — P, if possible.
P =
3 –2
1 0
2 –1
Q=4 7 2
5 1 –1R =
1 4
–2 3
0 4
= 3
1 4
–2 3
0 4
–
3 –2
1 0
2 –1
=
3(1) 3(4)
3(–2) 3(3)
3(0) 3(4)
–
3 –2
1 0
2 –1
=
3 12
–6 9
0 12
–
3 –2
1 0
2 –1
0 14
–7 9
–2 13
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
Lesson Quiz
1. What are the dimensions of A?
2. What is entry D12?
Evaluate if possible.
3. 2A — C 4. C + 2D 5. 10(2B + D)
–2
3 2
Not possible