GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 13 of 65

Marks: +1, -0

The rank of the matrix,

{M}=[\table 0 , 1 , 1 ; 1 , 0 , 1 ; 1 , 1 , 0]

, is

Solution:

Given matrix

{M}=(\table 0 , 1 , 1 ; 1 , 0 , 1 ; 1 , 1 , 0)

{R}_{3} ↔ {R}_{1}(\table 1 , 1 , 0 ; 1 , 0 , 1 ; 0 , 1 , 1)

{R}_{2} → {R}_{2}- {R}_{1}(\table 1 , 1 , 0 ; 0 , -1 , 1 ; 0 , 1 , 1)

{R}_{3} → {R}_{3}+ {R}_{2} \;\; (\table 1 , 1 , 0 ; 0 , -1 , 1 ; 0 , 0 , 2)

Rank = Number of Non zero rows in Echelon form

=3

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