1. 4.1: Matrix Operations Objectives: Students will be able to: Add, subtract, and multiply a matrix by a scalar Solve Matrix Equations Use matrices to organize data

2. Matrix A rectangular arrangement of numbers in rows and columns Dimensions of a Matrix: # rows by # columns 2 X 3 (read 2 by 3)

3. Entries: the numbers in a matrix Square Matrix: a matrix with the same # of rows and columns

4. What are the dimensions of the matrices below? 1.2.3.

5. Two matrices are equal if their dimensions are the same and the entries in corresponding positions are equal. Two matrices are equal if their dimensions are the same and the entries in corresponding positions are equal. Are the following matrices equal? 1. and 2. and

6. To add and subtract matrices, add or subtract corresponding entries:  Can only add and subtract if matrices have the same dimensions Perform the indicated operations: 1. 2. 3.

7. Scalar Multiplication: multiply each entry of the matrix by the scalar 1. 2.

8. Solving Matrix Equations: Solve for x and y 1. Method 1: Simplify inside parenthesis then multiply Method 2: Multiply scalar then add

9. Solve for x and y:

10. Properties of Matrix Operations: A, B and C are matrices, c is a scalar 1. Associative Property (regroup) 2. Commutative Property (change order) 3. Distributive Property of Addition 4. Distributive Property of Subtractions (A+B)+C = A +(B+C) A + B = B +A c(A +B) = cA + cB c(A- B) = cA- cB

11. Using Matrices to Organize Data: Use matrices to organize the following data about insurance rates. This year for 1 car, comprehensive, collision and basic insurance cost $612.15, $518.29 and $486.91. For 2 cars, comprehensive, collision and basic insurance cost $1150.32, $984.16, and $892.51. Next year for 1 car, comprehensive, collision and basic insurance will cost $616.28, $520.39, and $490.05. For 2 cars, comprehensive, collision and basic insurance will cost $1155.84, $987.72, and $895.13.

12. Use the matrices to write a matrix that shows the MONTHLY changes from this year to next.