Let T R → R" be a linear transformation, and let {₁,...,} be a set vectors in R". Prove that if {T(v₁),...,T(vp)} is linearly independent, then {v₁,...,Up} is linearly dependent.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Let T : R¹ → R™ be a linear transformation, and let {₁,..., vp} be a set vectors
in R". Prove that if {T(v₁),...,T(vp)} is linearly independent, then {v₁,...,Up} is linearly
dependent.
Transcribed Image Text:Let T : R¹ → R™ be a linear transformation, and let {₁,..., vp} be a set vectors in R". Prove that if {T(v₁),...,T(vp)} is linearly independent, then {v₁,...,Up} is linearly dependent.
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Step 1

Given that T:nm be a linear transformation, and v1, v2,....,vp be a set of vectors in n.

We have to prove that if Tv1, Tv2,....,Tvp is linearly independent, then v1, v2,....,vp is linearly independent.

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