1. In the following Question (a-b), a function T: VW between vector spaces and two vectors u and v in V are given. i. Find T(u) and T(v) ii. Is T(u + v) = T(u) + T(v)? iii. Is T a linear transformation? a) Define T(ax³ + bx² + cx + d) = [¯a −=b+¹], ₁ Let u = x³ + 2x² - x + 1 and v=x²-1 c+d 2 b) Define T: R³ → R² by T = ·()=[²+²]· Let u 2 v=

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Q: 2. Now let W be the line y = 2x in R². (a) Find a unit vector u on W. (b) Consider the linear…

A: Dear student as per our guidelines we can solve only first 3 questions. So kindly resubmit remaining…

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A: We will take an example to understand the situation better .

Q: Q3. a) Express the vector (4,2) e R' as linear combination of the vectors (1,1) and (1,-1). b) Let T…

A: We have to find all these

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A: The given vectors  and .To find the vector  and its additive inverse.

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Q: 3. Let B = Consider T : R2,2 → R²,² defined by T(A) = AB – BA. Let [o o] Bị and B2 :

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