MADEEASY TESTSERIES

Question

To justify the OPTION B they gave an example of 2*2 matrix. However we can see that row 2 is linearly dependent on row1. Even though the 2nd row looks non-zero it can be made into zero. SO am I wrong or the explanation is wrong?

Comments

@shishir__roy bro for option c answer would be min(n-k,k). right?

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@*nikhil* can you prove your claim?

Moreover, $rank(I_4 + 0) ≠ min(4,0)$

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okay i got it.so we can't comment anything on rank of A+B just from given information.and suppose instead of A+B we have AB then only we can write min(n-k, k)?

Answer 1

If determinant if A is equals to zero then only we can say rank less than order(i.e, rows are linearly dependent) but there is no relation between rows and rank.

Yes if after the row Matrix operations you get 1 row entirely becoming zero then we guarantee rank equals n-1