Publish On: 2019-04-18

# Guy white

Total Post: 819

## Question: What are equivalent matrices

Reply On: 2013-10-04

# Mjay Jollay

Total Post: 0

## ANS: What are equivalent matrices

Two matrices A and B are said to be equivalent, A ~ B, if one can be obtained from the other by a sequence of elementary transformations. Equivalent matrices have the same order and same rank.

The following results are obvious:

(a) Each matrix A is equivalent to itself, i.e. A ~ A.

(b) If a matrix B is equivalent to A, then A is also equivalent to B, i.e. A ~ B implies B ~ A.

(c) If a matrix C is equivalent to B, and B is equivalent to A, then C is equivalent to A, i.e. A ~

B and B ~ C imply A ~ C.

(d) If A and C are both equivalent to B, then they are equivalent to each other.

The following results are obvious:

(a) Each matrix A is equivalent to itself, i.e. A ~ A.

(b) If a matrix B is equivalent to A, then A is also equivalent to B, i.e. A ~ B implies B ~ A.

(c) If a matrix C is equivalent to B, and B is equivalent to A, then C is equivalent to A, i.e. A ~

B and B ~ C imply A ~ C.

(d) If A and C are both equivalent to B, then they are equivalent to each other.

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