Suppose a1,a2,........... real numbers, with a1≠0. If a1,a2,........... are in A.P, then

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A=a1a2a3a4a5a6a7a8a9 is singular

The system of equations a1x+a2y+a3z=0, a4x+a5y+a6z=0, a7x+a8y+a8z=0 has infinite number of solutions

B=a1ia2ia2a1 is non-singular ; where i=−1

None of these

answer is A.

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Detailed Solution

We have, |A|=a1a2a3a4a5a6a7a8a9=a1a2a33d3d3dddd=0 [Using R3→R3−R2 and R2→R2−R1] ∴ The given system of homogenous equations has infinite number of solutions.Also, |B|=a12+a22≠0. Thus,B is non-singular.

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