Short Answer

TRUE OR FALSE?
The formula rref(AB) = rref(A) rref(B) holds for all $n \times p$ matrices A and for all $p \times m$ matrices .

The given statement is true.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Reduce row echelon form

The reduced row echelon form of a matrix contains leading ones followed by zeros in each row with a shift in place of leading ones with every next row.

Step 2: Consider the parameters

The product of rref of matrices will result in either identity matrix or the identity matrix followed by rows of zeros.

Thus, the formula rref(AB) = rref (A) rref(B) holds good.

Hence, the statement is true.

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Linear Algebra With Applications

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Short Answer

TRUE OR FALSE?
The formula rref(AB) = rref(A) rref(B) holds for all $n \times p$ matrices A and for all $p \times m$ matrices .

Step by Step Solution

Step 1: Reduce row echelon form

Step 2: Consider the parameters

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Linear Algebra With Applications

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Short Answer

TRUE OR FALSE?The formula rref(AB) = rref(A) rref(B) holds for all n×p matrices A and for all p×m matrices .

Step by Step Solution

Step 1: Reduce row echelon form

Step 2: Consider the parameters

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TRUE OR FALSE?
The formula rref(AB) = rref(A) rref(B) holds for all $n \times p$ matrices A and for all $p \times m$ matrices .