Maths · The fundamental principle of counting
Assertion The possible dimension of a matrix consisting 27 elements is 4 Reason
Assertion The possible dimension of a matrix consisting 27 elements is 4 Reason The number of ways of expressing 27 as a product of two positive integers is 4
- A. Both Assertion \& Reason are individually correct \& Reason is correct explanation of Assertion,
- B. Both Assertion \& Reason are individually true but Reason is Not the correct explanation of Assertion
- C. Assertion is correct but Reason is incorrect
- D. Assertion is incorrect but Reason is correct.
Step-by-step solution
A matrix with 27 elements must have dimensions (rows × columns) such that product is 27. The ordered pairs of positive integers multiplying to 27 are (1,27), (3,9), (9,3), (27,1), so there are 4 possible dimensions. The Reason correctly counts these 4 ways. Hence both are true and Reason explains Assertion.
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