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Write a basis for a hyper plane in $\mathbb{R}^3$

A hyper plane in $R^3$ is,

$$\overrightarrow{x} = c_1<1, 0, 0> + c_2<0, 1 , 0>, c_1, c_2 \in \mathbb{R}$$

So I did some calculations with span and got that the the basis would be

$A = \{<1, 0 ,0>, <0, 1, 0> \}$

But that is literally almost the exact same thing?

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    It is expected to be the same thing, looking at the way it is defined. But then, the question seems too easy, so I'm wondering if you've missed some detail. – 2017-01-10

1 Answers 1

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The hyperplane is the set

$H=\{c_1<1, 0, 0> + c_2<0, 1 , 0>: c_1, c_2 \in \mathbb{R} \}$.

$H $ is a subspace of $ \mathbb R^3$. A basis of $H$ is given by $A = \{<1, 0 ,0>, <0, 1, 0> \}$, hence

$$H= span(A).$$