Let 2 x + a y + 6 z = 8 , x + 2 y + b z = 5 and x + y + 3 z = 4 be three equations. If these 3 equations are consistent, then

Question

Let 2 x + a y + 6 z = 8 , x + 2 y + b z = 5 and x + y + 3 z = 4 be three equations. If these 3 equations are consistent, then, b = 3 , a ≠ 2, a = 2 , b ≠ 3, a ≠ 2 , b ≠ 3, a ≠ 2 , b = 4

MARKS App · Accepted Answer

From Cramer’s rule, for consistent system △ = △ 1 = △ 2 = △ 3 = 0 △ = 2 a 6 1 2 b 1 1 3 = 2 6 − b − a 3 − b + 6 1 − 2 = 12 - 2 b - 3 a + a b - 6 = 6 - 2 b - 3 a + a b = a - 2 b - 3 △ 1 = 8 a 6 5 2 b 4 1 3 = 8 6 - b - a 15 - 4 b + 6 5 - 8 = 48 - 8 b - 15 a + 4 a b - 18 = 30 - 15 a - 8 b + 4 a b = ( 4 b - 15 ) ( a - 2 ) △ 2 = 2 8 6 1 5 b 1 4 3 = 2 15 - 4 b - 8 3 - b + 6 4 - 5 = 30 - 8 b - 24 + 8 b - 6 = 0 △ 3 = 2 a 8 1 2 5 1 1 4 = 2 8 - 5 - a 4 - 5 + 8 1 - 2 = a - 2 For consistent system a = 2

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