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Question

The rank of the matrix ⎢ ⎢ ⎢ ⎢ ⎢ ⎢1100000110011001000100011⎥ ⎥ ⎥ ⎥ ⎥ ⎥ is ____.
  1. 4

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Solution

The correct option is A 4
r1r2r3r4r5⎢ ⎢ ⎢ ⎢ ⎢ ⎢1100000110011001000100011⎥ ⎥ ⎥ ⎥ ⎥ ⎥

r1r1+r2+r3+r4+r5

We get,

A=⎢ ⎢ ⎢ ⎢ ⎢ ⎢0000000110011001000100011⎥ ⎥ ⎥ ⎥ ⎥ ⎥5×5

So, |A|=0
Hence rank(A)<5

But now another row is not becoming zero.
So at least one 4× 4 matrix in A is not zero
Hence Rank = 4



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