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suppose 1 2 3 4 5 6 7 8 9 is a matrix. Then what is its rank?
suppose 1 2 3
4 5 6
7 8 9
is a matrix. Then what is its rank?
Dear Sumit, Column rank is defined as maximum number of linearly independent columns. Row rank is defined as maximum number of linearly independent rows. In general both of them are equal, hence rank of a matrix = max no. of independent rows or columns. In the given matrix, any row cannot be obtained by the linear combination of remaining two rows, which means all the three rows are linearly independent, hence there are 3 independent rows which means Rank of the given matrix is 3 Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best Sumit !!!Regards,Askiitians ExpertsRohith Gandhi P
Dear Sumit,
Column rank is defined as maximum number of linearly independent columns.
Row rank is defined as maximum number of linearly independent rows.
In general both of them are equal, hence rank of a matrix = max no. of independent rows or columns.
In the given matrix, any row cannot be obtained by the linear combination of remaining two rows, which means all the three rows are linearly independent, hence there are 3 independent rows which means Rank of the given matrix is 3
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best Sumit !!!Regards,Askiitians ExpertsRohith Gandhi P
rank of the above matrix is 3
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