Warm-UP A = 7-310B = C =7-4Find:A 22 and C 31 97Find: the dimensions of each -88 Matrix Find: A + B and B – A and C + B

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.

Scalar Multiplication of Matrices

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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.

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

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

(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

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

Worksheet