Suppose A is nxn. the vectors not in col(a) form a subspace of R^n. True or False?

I believe it is false as the col(A) = Ax: x is an element or R^n, is a subspace of R^n. Is this right?

Question

Suppose A is nxn. the vectors not in col(a) form a subspace of R^n.  True or False?

I believe it is false as  the col(A) = Ax: x is an element or R^n, is a subspace of R^n.  Is this right?

amistre64 · Answer

without knowing the vectors that make up A its impossible to tell

anonymous · Answer

i thought col(A) forms the subspace of R^n

anonymous · Answer

I know it is true for a mxn matrix but is it different for a nxn?

amistre64 · Answer

hmm, each vector in its own right forms a vector space .... i might be confusing properties

amistre64 · Answer

a subspace of R^n would include lower ns right?

anonymous · Answer

that's what i'm confused about

amistre64 · Answer

what do remember about the properties of a subspace?

amistre64 · Answer

zero vector, closed under adding and multiplying right?

amistre64 · Answer

im thinking colA is a spans of R^n; and each vector is, in its own right, a vector subspace in R^n.  Unless im still reading it off, i think its true

anonymous · Answer

but do the vectors NOT in col(A) for a subspace?

anonymous · Answer

?

amistre64 · Answer

what would you define as a vector the is NOT in A ?

amistre64 · Answer

or even not in colA

amistre64 · Answer

the question just sounds off to me.

are we considering colA as being a basis for a vector space, or just a span of vectors that are linearly dependant or independant that form the columns of A?

anonymous · Answer

i messaged my prof.  he worded the question wrong.  thanks for you rhelp