# SOLUTION: Show that the rank of the transpose of the following matrix is the same as that of original matrix. 4 1 2 -3 2 4 8 -1 -2

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 Question 16090: Show that the rank of the transpose of the following matrix is the same as that of original matrix. 4 1 2 -3 2 4 8 -1 -2 Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!Show that the rank of the transpose of the following matrix is the same as that of original matrix. 4 1 2 -3 2 4 8 -1 -2 4 1 2 let -3 2 4 = A 8 -1 -2 4 -3 8 1 2 -1 = AT 2 4 -2 Rank of a matrix is the largest order of non zero determinant you can carve out from a matrix by deleting certain columns / rows so the situation does not change by taking a transpose of a matrix. so the rank of a matrix is always same as its transpose. in this case rank is 2 since the only one 3rd. Order determinant that can be formed is zero.we find non zero second order deteminants in A and its transpose. So their rank is same as 2 .