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Question

Is pivot columns and basic variables same thing?? or basic variables are the first elements of non zero rows in echelon matrics??

Answer 1

In summary, basic variables correspond to the pivot columns in a matrix reduced to its row echelon form. Each basic variable is associated with a specific pivot column and plays a key role in determining the solutions to the system of linear equations. So, while they are not precisely the same thing, they are closely related concepts in the context of solving systems of linear equations using matrices.