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Q.

Suppose the vectors X1,X2 and X3 are the solutions of the system of linear equations, AX=b when the vector B on the right side is equal to B1, B2 and B3 respectively. If X1=111,X2=021,X3=001,B1=100B2=020 and B3=002 , then the determinant of A is equal to

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a

4

b

32

c

12

d

2

answer is D.

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Detailed Solution

AX=BAX1=B1   Ax2=b2  Ax3=b3  Let A=ℓ1ℓ2ℓ3 m1 m2 m3n1n2n3AX3=B3 ⇒ℓ1ℓ2ℓ3 m1 m2 m3n1n2n3001=002ℓ3 m3n3=002ℓ3=0, m3=0,n3=2AX2=B2 ⇒ℓ1ℓ20 m1 m20n1n22021=0202ℓ22 m22n2+2=020 now AX3=B3ℓ100 m110n1-12111=100ℓ1=1 m1=-1n1=-1 A=100-110-1-12=2
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