5 minutes Warm-Up Evaluate each expression for a = -5, b = 1.3, and c = -7. 1) a + b 2) b - c 3) a – b + c 4) -4b Solve each equation. 5) 16 = 2x - 5 6) 3y + 8 = -y - 15

4.1.1 Using Matrices to Represent Data Objectives: Represent mathematical and real-world data in a matrix Find sums and differences of matrices and the scalar product of a number and a matrix

Matrices -useful for organizing data Jose and Janet sold candy bars for a recent fundraiser. Here is what they each sold: Snickers M&M’s 3 Musketeers Jose 8 5 12 Janet 6 9 7

Matrices A matrix is a rectangular array of numbers enclosed in a single set of brackets. The dimensions of a matrix are the number of horizontal rows and the number of vertical columns it has. Each number in the matrix is called an entry, or element. The address of each entry is its location in the matrix (rows then columns). m21 = 6 m22 = 9 m13 = 12

Example 1 The table shows the number of hours students studied math and science the week before midterm exams and the week before final exams. Before midterms Before finals Math 8 15 Science 7 12 a) Represent the number of hours studied in matrix T. b) Interpret the entry at t21. t21 = 7

Example 2 Solve for x and y. 4x + 5 = 21 -2y + 3 = y - 12 4x = 16

Practice Solve for x and y.

Example 3 a) Find M + N. M + N = -3 15 -1 33 9 3 b) Find M - N. -7 3 5 -11 -11 3

Practice a) Find A + B. b) Find A - B.

Homework p.