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  3. 3 consider the vector space r3 over r with the...

Question: 3 consider the vector space r3 over r with the...

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3. Consider the vector space R3 over R with the usual opcrations of scalar multiplication ard vector addition. Let a-(e! :-( 1,0, 0), e2 : (a) Give the definition of a linearly independent subset of R3 (b) Consider the linear transformation T : R3 → R3 whose action on the basis β = (0.1 , 0), e3 :-(0,0,1)). 0,1), (0, 1,1),(,0)) (you can take for granted that is a basis) is as follows: TU 1,0,1)) = (0,0,0), T((0, 1, 1)) = el, T((1,1,0)) e3- Write T((-1.-1.2)) as a linear combination of the vectors in the standard basis
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