Suppose that A is a 3 x 3 matrix whose nullspace is a line through the origin in 3-space. Can the row or column space of A also be a line through the origin?(adsbygoogle = window.adsbygoogle || []).push({});

Well if we have a matrix whose nullspace is a line through the origin then we have..

[X;Y;Z] = [a;b;c] t

And we know that the dimensions of our nullspace is 1..

Also we know that nullspace(a)+rank(a) = n

where n is the columns.

so..

1+rank(a)=3

this implies the rank = 2.

Which has a dimension of two, which means it is a plane through the origin. If the dimension was one, then we would have a line through the origin.

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# Homework Help: Another L.A. problem, am i doing this correcto?

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