Let T: P3 - P, be the linear map defined by T(p(x)) = xp'(x)-2p(x) (here p'(x) is the derivative of p(x)). Which of the following collections forms a basis for ker(T)? O { 1, x, x? } O {x, -3x2+x3 } O {x? } O { 1, -3x2+x³ } O{ -3x+x?, -3x2+x³ } What is nullity(T)? What is rank(T)?

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Q: 10) Show that [x] = −[−x] A 11) suppose that g: A → B and f: BC, where A = B = C = {1,2,3,4}, g =…

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A: We will draw the arrow diagram for function mapping from set A to set B.

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Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

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A: Given:

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Q: dependent.

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Q: mplify ƒ (x, y, z, w) to the simplest form. The Karnaugh map can b

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Q: 3. Describe the map T* if T = L(C³) is defined by T(x1, x2, x3) = (0,x1, x2).

A: Sure, so let's break it down. The map (T∗) here is a transformation that takes a point…