1. Algebra 2: Lesson 5 Using Matrices to Organize Data and Solve Problems

2. Warm-up p. 29 #1-5 1. The Additive _______ Property states that a + (-a) = 0 2. Add 16.5 – (-24.8) 3. Solve: 4 – 3y = 16 4. True or False: By the Commutative Property: j – k = k – j 5. Simplify: -4(x + 1)+ 3(2x – 7)

3. Warm-up p. 29 #1-5 1. The Additive Inverse Property states that a + (- a) = 0 2. Add 16.5 – (-24.8) 41.3 3. Solve: 4 – 3y = 16 4 – 16 = 3y; -12 = 3y; - 4=y 4. True or False: By the Commutative Property: j – k = k – j 5. Simplify: -4(x + 1)+ 3(2x – 7) -4x – 4 + 6x – 21 = 2x - 25

4. New Concept: Matrix A matrix is a rectangular array of numbers. The number of rows and columns in a matrix gives the dimensions of the matrix. A matrix with “r” rows and “c” columns is a matrix of dimension “r × c”. B = -3 -1 -2 2 -5 -4 Row #1 Row #2 Column #1 Column #3 Column #2

5. Give the dimensions of each matrix.

6. 3 × 2 4 × 1 2× 3

7. Elements of matrices Each member of the matrix is called an element and has a unique address. For example, in matrix A, a 43 is 5. What element is located at a 23 ?

8. Matrix Addition To add two matrices of the same dimension, add each element in the first matrix to the element that is in the same location in the second matrix.

9. Zero Matrix A zero matrix is formed when a matrix is added with its additive inverse matrix. matrix additive inverse matrix zero matrix

10. Matrix Subtraction To subtract two matrices of the same dimensions, A – B, take the opposite, or additive inverse, of B and add it to A.

11. Matrix Subtraction To subtract two matrices of the same dimensions, A – B, take the opposite, or additive inverse, of B and add it to A.

12. Example 2 Find the additive inverse matrix of A. Add: -A + B Subtract: A – B. A = -1 2 -5 0 -4 3 B = -3 -1 -2 2 -5 -4

13. Example 2 A = -1 2 -5 0 -4 3 B = -3 -1 -2 2 -5 -4 -A = 1 -2 5 0 4 -3 -A + B= -2 -3 3 2 -1 -7 A – B= 2 3 -3 -2 1 7

14. Ex. 3: Solving a Matrix Equation Rewrite the equation as a subtraction equation. Subtract the matrices. -5 2 -4 3 + X = -1 -2 -5 -4 -5 2 -4 3 = X -1 -2 -5 -4 – 4 -4 -1 -7 X =

15. Ex 4: Solving for Variables in Matrices Equal matrices have equal elements in matching locations. Write equations to make matching locations equal. a+12 = 18; a = 6 2b = -14; b = -7 23 = a + c; 23 = 6 + c; 23 - 6 = c; c = 17 d = 3b; d = 3(-7); d = -21 a + 12 2b 23 d = 18 -14 a + c 3b

16. Scalar Multiplication A scalar is a constant by which a matrix is multiplied. Scalar Multiplication is analogous to repeated Matrix Addition. To multiply matrix A by scalar “n”, multiply every element of A by n.

17. Ex. 4: Scalar Multiplication -5 2 -4 3 Evaluate : -2 M M =

18. Ex. 4: Scalar Multiplication -5 2 -4 3 -2 -10 -4 -8 -6 = -5 2 -4 3 Evaluate : -2 M M =

19. Partner Practice page 32 Lesson Practice a - f Individual Practice page 33 #1-29 odd