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The rank of the following matrix is [1, 1, 0, -2; 2, 0, 2, 2; 4, 1, 3, 1]

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

With R2->R2-2R1 = [0,-2,2,6] and R3->R3-4R1 = [0,-3,3,9], we find R3' = 1.5*R2', so the third row is linearly dependent. Only two independent rows remain, so the rank is 2.

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