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

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.

Kenny
RELATED QUESTIONS
If a matrix B results from a matrix A by applying an elementary row operation, is there... (answered by richwmiller)

if matrix B results from a matrix A by applying elementary row operation, is there always (answered by robertb)

Let A be an m x n matrix. Show that if A has linearly independent column vectors, then... (answered by robertb)

I am a bit overwhelmed by the complexity of this question. Please help me to understand... (answered by solver91311)

A"basic row operation"on a matrix means adding a multiple of one row to another row... (answered by ikleyn)

suppose A is a 4 x 2 matrix ,B is an r x s matrix and C is a 2 x 4 matrix. If... (answered by richard1234)

suppose A is a 4 x 2 matrix ,B is an r x s matrix and C is a 2 x 4 matrix. If... (answered by Fombitz)

2. (a) Prove that the product of a matrix and its transpose is symmetric matrix (b)... (answered by lynnlo)

A^T denotes the transpose of a matrix A. Show that = Tr(B^T,A) defines an inner... (answered by khwang)