B = (v1, v2 , v3) is a basis of a vector space V andT : V → V is a linear transformation which satisfies T(v1) = v1 + v2 + 2v3,T(v2) = 2vi + v2 + 3v3,T(v3) = v1 + 2v2 + 4v3. If u = 4v1 – v2 – v3 and T(u) = c1v1 + c2v2 + C3V3 then what is the value of c1 + c2 + c3? %3D - - O 4 O 2 O 5 3.

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A: Here we can use the composition of function formula to find the required values.

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A: See the detailed solution below.

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A: T(x1 , x2 , x3 , x4) = 3x1 + 4x2 - 3x3 + x4            = [3     4      -3     1] ((x1 , x2 , x3 ,…