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Inequalities Involving Modulus Function

Let A =[aij],...

Question

Let $A = [a_{i j}], 1 \leq i, j \leq n w i t h n \geq 3 a n d a_{i j} = i . j$ the rank of A is

A

0

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B

1

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C

n - 1

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D

n

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Solution

The correct option is B 1
Rank of A = 1

Because each row will be scalar multiple of first row. So we will get only one non-zero row in row Echelon from of A.

Alternative:

Rank of A = 1

Because all the minors of order greater than one will be zero

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