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

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 .

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