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Publish On: 2019-04-20

Guy white

Total Post: 819

Question: What are elementary matrices

Reply On: 2013-10-04

Mjay Jollay

Total Post: 0

ANS: What are elementary matrices

A matrix obtained from a unit matrix by performing on it a single elementary transformation is called an elementary matrix. Since unit matrices are always square, therefore elementary matrices will also be square matrices of the same order.

Remark: (i)  is an elementary matrix since it is obtained from I3 =  by performing R13
or C13. So R13 and C13 when operated on I3 give us the same elementary matrix.

(ii)  is an elementary matrix since it is obtained from I3 by performing R2 (7) or C2 (7). Thus R2 (7) and C2(7) when operated on I3 give us the same elementary matrix.

(iii)  is an elementary matrix obtained from I3 by performing R13 (4). The elementary matrix
obtained from I3 by performing C13 (4) will be  which is clearly the transpose of the matrix . Thus the elementary matrix obtained from I3 by performing C13 (4) is the transpose of the elementary matrix obtained from I3 by performing R13 (4).

Keeping these examples in mind, we give below standard notations for elementary matrices.
 

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