Let V be the vector space of polynomials in r with real coefficients of degree at most 3. So: V = {ao +a1x + a2x² + a3x° : ao, ɑ1, a2, a3 € R}. Let L : V → V be the linear transformation such that L(x*) = x³-i for i = 0, 1, 2, 3. xi-1 for i = 1, 2, 3, 4 and B (a) Let v; {v1, V2, V3, V4}. Calculate [L]g. (b) Let wi = 1 + x³, wz = 1 – x³, wz = x + x² and w, = x – x². For S = {w1,W2; W3, W4}, calculate [L]s.

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

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A: Given  be the set of all pairs  of real numbers together with the following operations:

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A: Consider the given matrix: 14-30-2-751-4-575

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A: From the given information we get:

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A: Given linear transformation: L: V →V defined by L(xi) = x3-i, i = 0, 1, 2, 3 a) B = {1, x, x2, x3}.…

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Q: Let V be a vector space, v, u € V, and let T₁ : V → V and T₂ : V → V be linear transformations such…

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

Q: Let V be a vector space, v, u € V, and let T₁: V → V and T₂: V → V be linear transformations such…

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Q: im(T1 + 14T) im(14T† + T2).

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