AP EAMCET202420 May 2024Evening ShiftMathematicsMatricesActual

If A= [a_ i j ], 1 i, j n with n 2 and a_ i j =i+j is a matrix, then the rank of A is

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Correct answer

C. 2

Step-by-step solution

Given that n 2 and a_ ij =i+j Case-1: Let n=2A= [ array ll 2 & 3 3 & 4 array ] |A|= | array ll 2 & 3 3 & 4 array |=8-1=-1 0 Case-2: Let n=3A= [ array lll 2 & 3 & 4 3 & 4 & 5 4 & 5 & 6 array ] |A|= | array lll 2 & 3 & 4 3 & 4 & 5 4 & 5 & 6 array |=0 Hence rank =2

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