Lesson 1 Contents Example 1Organize Data in a Matrix Example 2Dimensions of a Matrix Example 3Solve an Equation Involving Matrices

Example 1-1a College Kaitlin wants to attend one of three Iowa universities next year. She has gathered information about tuition (T), room and board (R/B), and enrollment (E) for the universities. Use a matrix to organize the information. Which university’s total cost is lowest? Iowa State University: T - $3132 R/B - $4432 E - 26,845 University of Iowa: T - $3204 R/B - $4597 E - 28,311 University of Northern Iowa: T - $3130 R/B - $4149 E - 14,106

Example 1-1b Organize the data into labeled columns and rows. ISU UI UNI TR/BE Answer:The University of Northern Iowa has the lowest total cost.

Example 1-1c Dining Out Justin is going out for lunch. The information he has gathered from the two fast-food restaurants is listed below. Use a matrix to organize the information. When is each restaurant’s total cost less expensive? Burger ComplexLunch Express Hamburger Meal $3.39 Hamburger Meal $3.49 Cheeseburger Meal $3.59 Cheeseburger Meal $3.79 Chicken Sandwich Meal $4.99 Chicken Sandwich Meal $4.89

Example 1-1d The Burger Complex has the best price for hamburgers and cheeseburgers. Lunch Express has the best price for chicken sandwiches. Answer: Burger Complex Lunch Express Hamburger Meal Cheese- burger Meal Chicken Sandwich Meal

Example 1-2a State the dimensions of matrix G if 4 columns 2 rows Answer:Since matrix G has 2 rows and 4 columns, the dimensions of matrix G are 2  4.

Example 1-2b State the dimensions of matrix G if Answer:3  2

Example 1-3a Solvefor x and y. Since the matrices are equal, the corresponding elements are equal. When you write the sentences to solve this equation, two linear equations are formed.

Example 1-3b Second equation This system can be solved using substitution. Substitute 3x – 2 for y. Distributive Property Add 4 to each side. Divide each side by 7.

Example 1-3c To find the value for y, substitute 1 for x in either equation. Substitute 1 for x. First equation Simplify. Answer:The solution is (1, 1).

Example 1-3d Solvefor x and y. Answer: (2, 5)

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