Basis maths-linear algebra-Q4

+1 vote

Which of the following statements, regarding row reduction of a matrix is True?

(A). All matrices can be row reduced into more than one matrix in Echelon form, using different sequence of row operations.

(B). All Nonzero matrices can be row reduced into more than one matrix in Echelon form, using different sequence of row operations.

(C). All matrices can be row reduced into more than one matrix in Reduced Echelon form, using different sequence of row operations.

(D). All Nonzero matrices can be row reduced into more than one matrix in Reduced Echelon form, using different sequence of row operations.

asked May 15 in Basic Maths by gbeditor (44,560 points)
reshown May 16 by gbeditor

1 Answer

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Best answer
Reduced echelon form is unique for any matrix. For Zero matrix, we have unique echelon form.

A matrix can be transformed into either Echelon form(EF) or Reduced echelon form(REF). REF is unique for any matrix, But EF is Not necessarily unique. For any Non-zero matrix we can have any number of EF.
EF is unique only for Zero matrix.
answered May 16 by deepak-gatebook (112,760 points)
selected Jun 12 by deepak-gatebook
I don't get the explanation - it says "Reduced echelon form is unique for any matrix". But in option B, they have talked about reducing in more than one matrix. Can you elaborate a bit...
A matrix can be transformed into either Echelon form(EF) or Reduced echelon form(REF). REF is unique for any matrix, But EF is Not necessarily unique. For any Non-zero matrix we can have any number of EF.
EF is unique only for Zero matrix.
Answer:
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