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Back to Range Space and Null Space

Exercise 1

Avg difficulty 3.0

Let h ⁣:P3→P4h\colon\mathcal{P}_{3}\to\mathcal{P}_{4} be given by p(x)↦x⋅p(x)p(x)\mapsto x\cdot p(x). Which of these are in the null space? Which are in the range space?

  • (a)  x3x^{3}     (b)  00     (c)  77     (d)  12x−0.5x312x-0.5x^{3}     (e)  1+3x2−x31+3x^{2}-x^{3}

Hefferon, Linear Algebra, Maps Between Spaces, Range Space and Null Space, Exercise 1

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.