1. Warm-UP A = 7-310B =-10-3 96-579-6 C =7-4Find:A 22 and C 31 97Find: the dimensions of each -88 Matrix Find: A + B and B – A and C + B

2. Multiplying a Matrix by a Scalar Multiply each element in the matrix by the scalar to create a solution matrix. The solution matrix will have the same dimensions as the original matrix.

3. Scalar Multiplication of Matrices

4. Practice 7 -10 8 -4 9 8 0 = -3 -6 11

5. Adding and Subtracting Matrices We can only add matrices of the same order. Matrix addition and subtraction are very simple; we just add or subtract the corresponding elements. The solution matrix will have the same order/dimensions.

6. Example 5 4 -7 0 10 3 + 11 2= 7 -24 11

7. Example 5 4 -7 0 10 3 - 11 2= 7 -2 4 11

8. Solve X – = for the matrix X. ALGEBRA 2 LESSON 4-2 Using Adding and Subtracting Matrices in Equations 2 5 3 –1 8 0 10 –3 –4 9 6 –9 X – + = + 2 5 3 –1 8 0 10 –3 –4 9 6 –9 2 5 3 –1 8 0 2 5 3 –1 8 0 2 5 3 –1 8 0 Add to each side of the equation. X – = 10 –3 –4 9 6 –9 2 5 3 –1 8 0 12 2 –1 8 14 –9 X = Simplify. 4-2

9. Solve the equation ALGEBRA 2 LESSON 4-2 Adding and Subtracting Matrices Since the two matrices are equal, their corresponding elements are equal. 2m – n –3 8 –4m + 2n = for m and n. 15 m + n 8 –30 2m – n = 15–3 = m + n–4m + 2n = –30 2m – n –3 8 –4m + 2n = 15 m + n 8 –30 4-2

10. (continued) ALGEBRA 2 LESSON 4-2 Adding and Subtracting Matrices The solutions are m = 4 and n = –7. Solve for m and n. 2m – n = 15 m + n = –3 3m = 12Add the equations. m = 4Solve for m. 4 + n = –3Substitute 4 for m. n = –7Solve for n. 4-2 Transparencies

11. Challenge Problem Find x and y in the following equation using what you know from Algebra and Matrix Operations….. 7 2x = 7 2y+3 8y -9 7x+2 -9

12. Worksheet