1. Let v1, . . . , vn be nonze

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January 18th, 2023

1. Let v1, . . . , vn be nonzero vectors such that each vi+1 hasmore leading 0s than vi . Show that vectors v1, . . . , vn arelinearly independent.

Answer:

Iam giving two different proofs first is by mathematical inductionand second by using echleon form property of matrices. Both proofsare correct. I prefer first one proved by mathematical induction.Please feel free to ask for any query and rate positively.

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