समीकरण ` 3x + y + 2z = 3, 2x - 3y - z = -3 ` और ` x + 2y + z = 4 ` में व x, y व z के मान क्रमशः होंगे

Options

A. ` x=3,y=2,z=-2`
B. ` x=2, y=1 , z=3`
C. ` x=2,y=-1,z=-3`
D. ` x=1, y=2,z=-1`

Answer

D

Explanation

दिया है , ` [{:(3,1,2),(2,-3,-1),(1,2,1):}]= D ` ( माना )
हल करने पर
` D = 3 ( -3+2) - 1 (2+1) +2 (4+3) , D = 8 `
` x = (D_(1))/D , y = (D_(2))/D " तथा " z = (D_(3))/D `
` :. D _(1) = |{:(3,1,2),(-3,-3,-1),(4,2,1):}|=8,`
` D _(2) = |{:(3,1,2),(2,-3,-1),(1,4,1):}|= 16 `
तथा ` D_(3) = |{:(3,1,3),(2,-3,-3),(1,2,4):}|= -8`
` :. x = 8/8 = 1, `
` y = 16/2 = 2 `
तथा ` z = (-8)/8 = -1 `