4-1 Matrices and Data Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2

Warm Up Distribute. 1. 3(2x + y + 3z) 2. –1(x – y + 2) 6x + 3y + 9z –x + y – 2

Objectives Use matrices to display mathematical and real-world data. Find sums, differences, and scalar products of matrices.

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.

Matrix A has two rows and three columns 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.

You can add or subtract two matrices only if they have the same dimensions.

Example 2B: Finding Matrix Sums and Differences Add or subtract, if possible. 3 –2 1 0 4 7 2 5 1 –1 1 4 –2 3 2 –2 3 1 0 4 W = , X = , Y = , Z = X – Z Subtract each corresponding entry. 4 7 2 5 1 –1 2 –2 3 1 0 4 – 2 9 –1 4 1 –5 = X – Z =

Example 4A: Simplifying Matrix Expressions 3 –2 1 0 2 –1 1 4 –2 3 0 4 4 7 2 5 1 –1 P = Q= R = Evaluate 3P — Q, if possible. P and Q do not have the same dimensions; they cannot be subtracted after the scalar products are found.

Example 4B: Simplifying Matrix Expressions 3 –2 1 0 2 –1 1 4 –2 3 0 4 4 7 2 5 1 –1 P = Q= R = Evaluate 3R — P, if possible. = 3 1 4 –2 3 0 4 – 3 –2 1 0 2 –1 = 3 12 –6 9 0 12 – 3 –2 1 0 2 –1 3(1) 3(4) 3(–2) 3(3) 3(0) 3(4) – 3 –2 1 0 2 –1 0 14 –7 9 –2 13 =

Check It Out! Example 4b 4 –2 –3 10 4 –1 –5 3 2 8 3 2 0 –9 D = [6 –3 8] A = B = C = 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

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) 3  2 –2 Not possible