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Chapter Menu Lesson 4-1Lesson 4-1Introduction to Matrices Lesson 4-2Lesson 4-2Operations with Matrices Lesson 4-3Lesson 4-3Multiplying Matrices Lesson 4-4Lesson 4-4Transformations with Matrices Lesson 4-5Lesson 4-5Determinants Lesson 4-6Lesson 4-6Cramer's Rule Lesson 4-7Lesson 4-7Identity and Inverse Matrices Lesson 4-8Lesson 4-8Using Matrices to Solve Systems of Equations

Lesson 1 Menu Five-Minute Check (over Chapter 3) Main Ideas and Vocabulary Example 1: Real-World Example: Organize Data into a Matrix Example 2: Dimensions of a Matrix Example 3: Solve an Equation Involving Matrices

Lesson 1 MI/Vocab matrix element dimension row matrix column matrix square matrix zero matrix Organize data in matrices. Solve equations involving matrices. equal matrices

Lesson 1 Ex1 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 universitys total cost is lowest? Iowa State University: T - $5426R/B - $5958E - 26,380 University of Iowa: T - $5612R/B - $6560E - 28,442 University of Northern Iowa: T - $5387R/B - $5261E - 12,927 Organize Data into a Matrix

Lesson 1 Ex1 Organize the data into labeled columns and rows. Answer: The University of Northern Iowa has the lowest total cost. Organize Data into a Matrix ISU UI UNI TR/BE

Lesson 1 CYP1 DINING OUT Justin is going out for lunch. The information he has gathered from two fast-food restaurants is listed below. Use a matrix to organize the information. When is each restaurants total cost less expensive?

A.A B.B C.C D.D Lesson 1 CYP1 A.The Burger Complex has the best price for chicken sandwiches. The Lunch Express has the best prices for hamburgers and cheeseburgers. B.The Burger Complex has the best price for hamburgers and cheeseburgers. The Lunch Express has the best price for chicken sandwiches. C.The Burger Complex has the best price for chicken sandwiches and hamburgers. The Lunch Express has the best prices for cheeseburgers. D.The Burger Complex has the best price for cheeseburgers. The Lunch Express has the best price for chicken sandwiches and hamburgers.

Lesson 1 Ex2 Dimensions of a Matrix Answer: Since matrix G has 2 rows and 4 columns, the dimensions of matrix G are 2 × 4. 4 columns 2 rows State the dimensions of matrix G if

Lesson 1 CYP2 1.A 2.B 3.C 4.D A.2 × 3 B.2 × 2 C.3 × 2 D.3 × 3 State the dimensions of matrix G if G =

Lesson 1 Ex3 Solve an Equation Involving Matrices Since the matrices are equal, the corresponding elements are equal. When you write the sentences to solve this equation, two linear equations are formed. y=3x – 2 3=2y + x

Lesson 1 Ex3 Solve an Equation Involving Matrices This system can be solved using substitution. 3=2y + xSecond equation 3=2(3x – 2) + xSubstitute 3x – 2 for y. 3=6x – 4 + xDistributive Property 7=7xAdd 4 to each side. 1=xDivide each side by 7.

Lesson 1 Ex3 Solve an Equation Involving Matrices To find the value for y, substitute 1 for x in either equation. y=3x – 2First equation y=3(1) – 2Substitute 1 for x. y=1Simplify. Answer: The solution is (1, 1).

1.A 2.B 3.C 4.D Lesson 1 CYP3 A.(2, 5) B.(5, 2) C.(2, 2) D.(5, 5)

End of Lesson 1

Lesson 2 Menu Five-Minute Check (over Lesson 4-1) Main Ideas and Vocabulary Key Concept: Addition and Subtraction of Matrices Example 1: Add Matrices Example 2: Subtract Matrices Example 3: Real-World Example Key Concept: Scalar Multiplication Example 4: Multiply a Matrix by a Scalar Concept Summary: Properties of Matrix Operations Example 5: Combination of Matrix Operations

Lesson 2 MI/Vocab scalar scalar multiplication Add and subtract matrices. Multiply by a matrix scalar.

Lesson 2 KC1

Lesson 2 Ex1 Add Matrices Definition of matrix addition Add corresponding elements. Simplify. Answer:

Lesson 2 Ex1 Add Matrices Answer: Since the dimensions of A are 2 × 3 and the dimensions of B are 2 × 2, these matrices cannot be added.

A.A B.B C.C D.D Lesson 2 CYP1 A. B. C. D.

A.A B.B C.C D.D Lesson 2 CYP1 A. B. C. D.

Lesson 2 Ex2 Subtract Matrices Definition of matrix subtraction Subtract corresponding elements. Simplify. Answer:

Lesson 2 CYP2 1.A 2.B 3.C 4.D A. B. C. D.

Lesson 2 Ex3 SCHOOL ATHLETES The table below shows the total number of student athletes and the number of female athletes in three high schools. Use matrices to find the number of male athletes in each school.

Lesson 2 Ex3 The data in the table can be organized into two matrices. Find the difference of the matrix that represents the total number of athletes and the matrix that represents the number of female athletes. Subtract corresponding elements. totalfemalemale

Lesson 2 Ex3 Answer: There are 582 male athletes at Jefferson, 286 male athletes at South, and 677 male athletes at Ferguson.

Lesson 2 CYP3 TESTS The table below shows the percentage of students at Clark High School who passed the 9th and 10th grade proficiency tests in 2001 and Use matrices to find how the percentage of passing students changed from 2001 to 2002.

Lesson 2 CYP3 1.A 2.B 3.C 4.D A.B. C.D. 9 th grade10 th grade Math Reading Science Citizenship Math Reading Science Citizenship Math Reading Science Citizenship Math Reading Science Citizenship 9 th grade10 th grade 9 th grade10 th grade9 th grade10 th grade

Lesson 2 KC2

Lesson 2 Ex4 Substitution Multiply a Matrix by a Scalar

Lesson 2 Ex4 Multiply each element by 2. Multiply a Matrix by a Scalar Answer: Simplify.

A.A B.B C.C D.D Lesson 2 CYP4 A.B. C.D.

Lesson 2 CS1

Lesson 2 Ex5 Perform the scalar multiplication first. Then subtract the matrices. Combination of Matrix Operations Substitution Multiply each element in the first matrix by 4 and each element in the second matrix by 3. 4A – 3B

Lesson 2 Ex5 Combination of Matrix Operations Simplify. Subtract corresponding elements. Answer: Simplify.

A.A B.B C.C D.D Lesson 2 CYP5 A. B. C. D.

End of Lesson 2