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Exercise 2.6.8

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Every plane could be written in the form $P = {(x, y, z) : ax + by + cz = 0}$ for some scalar $a$ , $b$ and $c$ . Consider a transformation $T (x, y, z) = ax + by + cz$ . It can be shown that $T$ is an element in ${(ℝ^{3})}^{∗}$ and $P = N (T)$ . For the case in $ℝ^{2}$ , actually every line has the form $L = {(x, y) : ax + by = 0}$ and hence is the null space of a vector in ${(ℝ^{2})}^{∗}$ .

jephianlin

2011-06-27 00:00

Exercise 2.6.8

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