AI Tutor
Back to Range Space and Null Space

Exercise 9

Avg difficulty 3.0

For the homomorphism h ⁣:P3→P3h\colon\mathcal{P}_{3}\to\mathcal{P}_{3} given by h(a0+a1x+a2x2+a3x3)=a0+(a0+a1)x+(a2+a3)x3h(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3})=a_{0}+(a_{0}+a_{1})x+(a_{2}+a_{3})x^{3} find these.

  • (a)  N(h)\mathscr{N}(h)     (b)  h−1(2−x3)h^{-1}(2-x^{3})     (c)  h−1(1+x2)h^{-1}(1+x^{2})

Hefferon, Linear Algebra, Maps Between Spaces, Range Space and Null Space, Exercise 9

AI Tutor

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