For a system of linear equations represented by with square matrix

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

For a system of linear equations represented by AX=BAX=B with square matrix AA, which of the following conditions guarantees that the system is inconsistent (has no solution)? (a) ∣A∣=0|A|=0 (b) ∣A∣=0 and (adjA)B≠0|A|=0 \text{ and } (\mathrm{adj}A)B\neq 0 (c) ∣A∣≠0|A|\neq 0 (d) ∣A∣=0 and (adjA)B=0|A|=0 \text{ and } (\mathrm{adj}A)B=0

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