GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 61 of 65

Marks: +1, -0

The rank of the following matrix is

(\table 1 , 1 , 0 , -2 ; 2 , 0 , 2 , 2 ; 4 , 1 , 3 , 1)

Solution:

A=(\table 1 , 1 , 0 , -2 ; 2 , 0 , 2 , 2 ; 4 , 1 , 3 , 1)

R_{2} → R_{2}-2 R_{1}, R_{3} → R_{3}-4 R_{1}

(\table 1 , 1 , 0 , -2 ; 0 , -2 , 2 , 6 ; 0 , -3 , 3 , 9)

R_{3} → R_{3}-\;{3}/{2} R_{2}

(\table 1 , 1 , 0 , -2 ; 0 , -2 , 2 , 6 ; 0 , 0 , 0 , 0)

No. of non zero rows

=2

rank of

A=2

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