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