Ex 3.1, 6 (ii) - Chapter 3 Class 12 Matrices

Transcript

Ex 3.1 , 6 Find the value of x, y, and z from the following equation: (ii) [■8(x+y&2@5+z&xy)] = [■8(6&2@5&8)] Since matrices are equal. Their corresponding elements are equal x + y = 6 5 + z =5 xy = 8 Solving these equations From (2) 5 + z = 5 z = 5 – 5 z = 0 From (1) x + y = 6 x = 6 – y From (3) xy = 8 Putting x = 6 – y (6 – y) y = 8 6y – y2 = 8 y2 – 6y = - 8 y2 – 6y + 8 = 0 y2 – 4y – 2y + 8 = 0 y2 (y – 4) –2(y – 4) = 0 (y – 2) (y – 4) = 0 Hence y = 2 and y = 4 Hence x = 2, y = 4 , z = 0 or x = 4, y = 2, z = 0 When y = 2 x = 6 – y x = 6 – 2 x = 4 When y = 4 x = 6 – y x = 6 – 4 x = 2