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Exercise 6

Avg difficulty 3.0

Decide if each changes bases on R2\mathbb{R}^{2}. To what basis is E2{\cal E}_{2} changed?

  • (a)  (5004)\begin{pmatrix}5&0\\ 0&4\end{pmatrix}     (b)  (2131)\begin{pmatrix}2&1\\ 3&1\end{pmatrix}     (c)  (−142−8)\begin{pmatrix}-1&4\\ 2&-8\end{pmatrix}     (d)  (1−111)\begin{pmatrix}1&-1\\ 1&1\end{pmatrix}

Hefferon, Linear Algebra, Maps Between Spaces, Changing Representations of Vectors, Exercise 6

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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.