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Warm-UP A= 7 9 C= 7 9 -8 -3 6 -4 7 8 10 -5 B= -1 7 0 9 -3 -6 Find: A22 and C31 Find: the dimensions of each Matrix Find: A + B and B – A and C + B Practice in Pairs • When businesses deal with sales, there is a need to organize information. For instance, let's say Karadimos King is a fast-food restaurant that made the following number of sales: • On Monday, Karadimos King sold 35 hamburgers, 50 sodas, and 45 fries. On Tuesday, it sold 120 sodas, 56 fries, and 43 hamburgers. On Wednesday, it sold 15 fries, 12 hamburgers, and 19 sodas. Create a matrix to hold this information. Transpose Matrix: A matrix which is formed by turning all the rows of a given matrix into columns and vice-versa. The transpose of matrix A is written AT. 1 4 1 2 3 T is 2 5 4 5 6 3 6 Equal Matrices: Two matrices are equal if they have the same dimensions and the corresponding elements are equal. 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 2 8 4( 2 ) 4( 8 ) 8 32 4 5 7 4( 5 ) 4( 7 ) 20 28 15 12 10 3( 15 ) 3( 12 ) 3( 10 ) 45 36 30 3 10 20 0 3( 10 ) 3( 20 ) 3( 0 ) 30 60 0 5 2 6 3( 5 ) 3( 2 ) 3( 6 ) 15 6 18 Practice 7 -10 8 9 8 0 -3 -6 11 -4 = 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. Example 5 4 10 3 7 -2 -7 + 0 11 2 4 11 = Example 5 4 10 3 7 -2 -7 - 11 4 0 2 11 = Using Adding and Subtracting Matrices in Equations ALGEBRA 2 LESSON 4-2 Solve X – X – X – 2 5 3 –1 8 0 + 2 5 3 –1 8 0 2 5 3 –1 8 0 2 5 3 –1 8 0 = = 10 –3 –4 9 6 –9 = 10 –3 –4 9 6 –9 10 –3 –4 9 6 –9 + for the matrix X. 2 5 3 –1 8 0 Add 2 5 3 –1 8 0 to each side of the equation. X = 12 2 –1 8 14 –9 4-2 Simplify.