SOLUTION: Let A be an m x n matrix. Prove that if B can be obtained from A by an elementary row (column) operation, then B transpose can be obtained from
A transpose by the corresponding e
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A transpose by the corresponding e
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Question 4520: Let A be an m x n matrix. Prove that if B can be obtained from A by an elementary row (column) operation, then B transpose can be obtained from
A transpose by the corresponding elementary column (row) operation. Answer by khwang(438) (Show Source):
You can put this solution on YOUR website! Proof: If B = EA, where E is a matrix of an elementary row (column) operation,
then transpose of B, B^T = (EA)^T = A^TE^T .
Since the transpose of a row(column) operation is a column(row) operation.
we see that E^T will be a matrix of an elementary column (row) operation,
B transpose can be obtained from A transpose by the corresponding elementary column (row) operation.
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