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Practice question

MCQ

Question

Consider the below statements - (i) For a matrix system AX = B, there will be a unique solution only iff |A| ≠ 0. (ii) A system of equations will always be inconsistent if |A| = 0. (iii) If |A| = 0 and (adjA)B = 0, then the system will have infinite solutions. (iv) For consistency |A| will always be non-zero. Then which of the following statements are true?

Options

Choose one · Correct answer highlighted

Explanation

Look at it this way: rule: unique iff |A|≠0. If |A|=0 and (adjA)B=0, you get infinite solutions. So i and iii correct. Full logic.

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