Consider the column vectors V = -0--0---0 V2= 1 and V3 (a) Explain why these...

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Consider the column vectors V₁ = Ο -0--0---0 V2= 1 and V3 (a) Explain why these column vectors are linearly independent. (b) Explain why these column vectors span R³. (c) Write e1, e2 and е3 as linear combinations of V1, V2 and V3 2 (d) Let T R³ → R³ be a linear transformation such that T(v1) T(v3): = 1. Use part (c) to determine T(e1), T(e2) and T(e3). (e) Is T onto? Justify your answer. (2). = 0 T(V2) = 2 and Consider the column vectors V₁ = Ο -0--0---0 V2= 1 and V3 (a) Explain why these column vectors are linearly independent. (b) Explain why these column vectors span R³. (c) Write e1, e2 and е3 as linear combinations of V1, V2 and V3 2 (d) Let T R³ → R³ be a linear transformation such that T(v1) T(v3): = 1. Use part (c) to determine T(e1), T(e2) and T(e3). (e) Is T onto? Justify your answer. (2). = 0 T(V2) = 2 and