2 Attachment(s)

gaussian and linear indep

Hello smart people,

I am having some concept difficulty.

This is what I dont understand......

Determine the column space of AAttachment 28813(see image above)

Use Gaussian elimination to check whether or not an arbitrary vector x

Please see the following picture insert.

Attachment 28812corresponds to a plane in R^3.Any basis of R^3 contains three vectors. Thus the four columns of A do not form a basis.(so its not a basis because there should be 3 vectors instead of 4.)

also that y =( insert pic-plz see above) is the cartesian equation of a plane in 3-dimensional space, and

only those vectors corresponding to a point on the plane are in the column space. So there arevectors in R^3 that do not belong to Col(A). (I dont understand how ther are vectors that dont belong in R^3?), Col(A) does not span R ..and hence is nota basis.(Since Col(A) is spanned by only two vectors, at most two of the columns of A form a linearly

independent set.)

1 Attachment(s)

Re: gaussian and linear indep

Hi n22,

The question is to give a __geometric__ argument for the column space. The attachment repeats your algebraic argument, but then does give a geometric argument:

Attachment 28822