Editing Row and column spaces (section)

==== Example ====
If <math>A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 2 & 0 \end{bmatrix}</math>, then the column vectors are {{math|1='''v'''<sub>1</sub> = [1, 0, 2]<sup>T</sup>}} and {{math|1='''v'''<sub>2</sub> = [0, 1, 0]<sup>T</sup>}}.
A linear combination of '''v'''<sub>1</sub> and '''v'''<sub>2</sub> is any vector of the form
<math display="block">c_1 \begin{bmatrix} 1 \\ 0 \\ 2 \end{bmatrix} + c_2 \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} c_1 \\ c_2 \\ 2c_1 \end{bmatrix}</math>
The set of all such vectors is the column space of {{mvar|A}}. In this case, the column space is precisely the set of vectors {{math|(''x'', ''y'', ''z'') ∈ '''R'''<sup>3</sup>}} satisfying the equation {{math|1=''z'' = 2''x''}} (using [[Cartesian coordinates]], this set is a [[plane (mathematics)|plane]] through the origin in [[three-dimensional space]]).