.which of the following are spanning sets for R3. {(2,1,-2)transpose (3,2,-2)transpose (2,2,0)transpose} solution plz

Question

anonymous · Answer

Well, that's only one set.  Do you mean to ask if that is a spanning set of R3?

anonymous · Answer

yes plz show with solution

anonymous · Answer

How many linearly independent vectors do you need to span R3?

anonymous · Answer

i dont know perhaps three

anonymous · Answer

That is correct.  Now, what do you know about the determinant of a matrix that has linearly dependent columns?

anonymous · Answer

no

anonymous · Answer

Well, that wasn't really a yes or no question...

anonymous · Answer

But the determinant of such a matrix is zero.  So how about we arrange those three vectors in the columns of a matrix, and then take the determinant?  If it's zero, then they are linearly dependent, so they are NOT a spanning set.  Otherwise, we're good to go.

anonymous · Answer

thank you