Adding and Subtracting Matrices Algebra 2 4 2

Adding and Subtracting Matrices Algebra 2 4 -2 Adding and Subtracting Matrices cont.

Adding and Subtracting Matrices Lesson 4 -2 Algebra 2 Additional Examples Solve X – X – 2 5 3 – 1 8 0 + 2 5 3 – 1 8 0 = = 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 Simplify.

Adding and Subtracting Matrices Algebra 2 Solve X – 4 1 3 5 = 2 0 7 6 for the matrix X. Solve X – 1 3 1 2 = 0 8 1 9 for the matrix X.

Adding and Subtracting Matrices Lesson 4 -2 Algebra 2 Additional Examples Determine whether the matrices in each pair are equal. a. M = 8 + 9 5 – 6 – 1 ; 0 0. 7 8 + 9 5 – 6 – 1 0 0. 7 ; N = 17 4 – 10 0 5 – 2 + 1 – 7 9 7 Both M and N have three rows and two columns, but – =/ 0. 7. 9 M and N are not equal matrices.

Adding and Subtracting Matrices Lesson 4 -2 Algebra 2 Additional Examples (continued) b. P = 3 40 – 4 ; – 3 Q = 27 9 – 16 4 8 0. 2 – 12 4 Both P and Q have two rows and two columns, and their corresponding elements are equal. P and Q are equal matrices.

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

Adding and Subtracting Matrices Lesson 4 -2 Algebra 2 Additional Examples (continued) Solve for m and n. 2 m – n = 15 m + n = – 3 3 m = 12 m = 4 4 + n = – 3 n = – 7 Add the equations. Solve for m. Substitute 4 for m. Solve for n. The solutions are m = 4 and n = – 7.