Let A, B be m x n matrices over a field F such that their reduced...

  

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Let A, B be m x n matrices over a field F such that their reduced row- echelon forms are the same. What can we say about the relationship between the nullspace N(A) N(LA) of A and the nullspace N(B) = N(LB) of B? (2) Consider a non-linear operation on the following system of equations x(x + 2y) 3x + 4y X + 2y = 2 3x + = 0 = = 2x 0 Show that non-linear operations can change the set of solutions by com- paring two sets of solutions corresponding to the above systems. Let A, B be m x n matrices over a field F such that their reduced row- echelon forms are the same. What can we say about the relationship between the nullspace N(A) N(LA) of A and the nullspace N(B) = N(LB) of B? (2) Consider a non-linear operation on the following system of equations x(x + 2y) 3x + 4y X + 2y = 2 3x + = 0 = = 2x 0 Show that non-linear operations can change the set of solutions by com- paring two sets of solutions corresponding to the above systems.

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1 If the reduced rowechelon forms of matrices A and B are the same it means that they have the same row space and thus represent the same linear trans... View the full answer