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Thread: Independent v.s. dependent columns

  1. #1
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    Question Independent v.s. dependent columns

    Hi,

    I'm lost with this image:

    Independent v.s. dependent columns-screen-shot-2017-10-10-11.06.30-pm.png

    Can someone please explain the description of Figure 4.7? How is a1, a2, and a3 not in a plane while c1, c2, and c3 in the same plane? I struggling to find the reasoning behind this.

    (Sorry I forgot to convert the "1" in "a1" and the "2" and "a2" etc as subscripts)

    Appreciate help!

    - Olivia
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  2. #2
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    Re: Independent v.s. dependent columns

    what exactly don't you understand?

    The $a's$ are stated to be linearly independent and thus they span the entire 3D space

    The $c's$ are stated to be linearly dependent and thus they span a 2D space

    I can see that the drawing of the $c's$ looks a bit odd but just accept that they all lie in the same plane.
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