Question

please help!
Is the vector(4,5,1) in the span of the set consisting of(3,5,-4), (2,1,-5), and (-2,1,3)?
thanks ion andvance!!!!

Answer 1

yes, it is, and the transformation matrix is \[\left(\begin{matrix}2 \\ -3\\-2\end{matrix}\right)\]
it means 2(3,5,-4)-3(2,1,-5) -2(-2,1,3) = (4,5,1)
hope this helps

Answer 2

Thank you Hoa. may you uplaod the picture of your working so that i may able to fallow please

Answer 3

oh, I use math tool to find out the rref of matrix I construct, then take the result from it. the key point is construct that matrix. do you know how to do ?

Answer 4

i don't know, please help!

Answer 5

ok, you just put 4 vectors in order like c1,c2,c3 and the last one is the vector you want to know whether it can be span by other three or not. from yours, it should be

and then , if you know how to get rref by hand, do it, if not, put it into the link http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi to calculate the rref, the last column is your answer, put value of that column respectively to the 3 vectors to span it.