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Linear Algebra-Uniqueness of rref

  • Thread starter Roni1985
  • Start date
  • #1
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Homework Statement



"Prove a specific rref matrix is unique"

Homework Equations





The Attempt at a Solution



This is all I have on my review sheet for my next exam. I have the proof of the uniqueness of rref but how do you prove a specific rref matrix is unique ?

say that's any nonsingular matrix in R^3
Would appreciate any hints.

Thanks,
Roni.
 

Answers and Replies

  • #2
699
5
If the system is unique, we know it is nonsingular. What does a nonsingular rref matrix look like? It is a diagonal matrix with 1s in the diagonals or identity matrix.

Also, if the nxn matrix is unique, the column vectors are linearly independent.
 

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