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Question 4.7.1: Coordinates and Components in R^n Find the coordinate matrix...

Coordinates and Components in R^n

Find the coordinate matrix of x = (-2, 1, 3) in R³ relative to the standard basis

S = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}.

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Because x can be written as x = (-2, 1, 3) = -2(1, 0, 0) + 1(0, 1, 0) + 3(0, 0, 1), the coordinate matrix of relative to the standard basis is simply

[x]_s = \left [ \begin{matrix} -2 \\ 1 \\ 3 \end{matrix} \right ] .
So, the components of x are the same as its coordinates relative to the standard basis.

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