Let V be an n-dimensional vector space over F, and T:V→V be a linear transformation of rank 2. Prove that if v, w e Fª are two linearly independent rows, then there exists bases B,y of V so that v, w are the first two rows of T] and all other rows are zero.

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A: Given: Tx1,x2,x3=2x3-x2b1-2x3b2+x1+3x2b3 a. Te1=T1,0,0=0b1+0b2+1b3 Te2=T0,1,0=-1b1+0b2+3b3…

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Q: Let V be a finite-dimensional vector space over F, and let S,T € L(V) be linear operators on V with…

A: Consider the provided question,

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A: Given the linear transformation T:R3→V s.t.  Tx1,x2,x3=x2-x3b1+x1+x3b2+x2-x1b3, where E=e1,e2,e3 is…

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Q: Let T : V → V be a linear transformation. Carefully prove that the image of T is a subspace of V.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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