Question

Set of equations a+b-2c=0, 2a-3b+c=0 and a-5b+4c=alpha is consistent for alpha equals to (A) 1 (B) 0 (C) -1 (D) 2

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Set of equations a + b - 2c = 0, 2a - 3b + c = 0 and a - 5b + 4c = α is consistent for α equals to

(A) 1

(B) 0

(C) - 1

(D) 2

EVALUATION

Let the given Set of equations

a + b - 2c = 0, 2a - 3b + c = 0 and a - 5b + 4c = α

are consistent

$\sf{ \therefore \: \: \Delta_x = 0}$

$\displaystyle \implies \: \begin{vmatrix} 1 & - 2 & 0\\ - 3 & 1 & 0 \\ - 5 & 4 & \alpha \end{vmatrix} = 0$

$\displaystyle \sf{\implies \:1( \alpha - 0) - 2( - 3 \alpha - 0) + 0 = 0}$

$\displaystyle \sf{\implies \:7 \alpha = 0}$

$\displaystyle \sf{\implies \: \alpha = 0}$

FINAL ANSWER

Hence the correct option is (B) 0

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