In: Advanced Math
1. Let v1, . . . , vn be nonzero vectors such that each vi+1 has more leading 0s than vi . Show that vectors v1, . . . , vn are linearly independent.
I
am giving two different proofs first is by mathematical induction
and second by using echleon form property of matrices. Both proofs
are correct. I prefer first one proved by mathematical induction.
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