The rank of the matrix [\table -4 , 1 , -1 ; -1 , -1 , -1 ; 7 , -3 , 1] is

GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 25 of 65

Marks: +1, -0

The rank of the matrix

[\table -4 , 1 , -1 ; -1 , -1 , -1 ; 7 , -3 , 1]

Solution:

Converting the matrix into Echelon form,

[\table -4 , 1 , -1 ; -1 , -1 , -1 ; 7 , -3 , 1]

R_{1} ⟷R_2[\table -1 , -1 , -1 ; -4 , 1 , -1 ; 7 , -3 , 1]

R_{2}-4 R_{1} R_{3}+7 R_{1}[\table -1 , -1 , -1 ; 0 , 5 , 3 ; 0 , -10 , -6]

[\table -1 , -1 , -1 ; 0 , 5 , 3 ; 0 , 0 , 0]

Now since the matrix is in Echelon
Rank = Number of non-zero rows = 2

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