55 730
Assignments Done
97,1%
Successfully Done
In November 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Linear Algebra Question for Muhammad Imran Qureshi

Question #7979
Find one vector in R^3 that spans the intersection of U and W where U is the xy-plane, U={(a,b,0)}, and W is the space spanned by the vectors (1,1,1) and (1,2,3).
Expert's answer
Let u=(a,b,c) be the vector spanning the intersection of U and W.

First
we find the equation of the plane W spanned by the vectors v=(1,1,1) and
w=(1,2,3).
The normal vector, n=(nx,ny,nz), to this plane is the
cross-product n=[v,w].
This vector has the following
coordinates:


nx = det 1 1 = 3-2 = 1
2 3


ny
= det 1 1 = 1-3 = -2
3 1


nz = det 1 1 = 2-1 =
1
1 2


Thus n=(1,-2,1) and the equation of the plane
W:
x-2y+z=0

Thus u satisfies the equation:

a-2b+c=0.

Moreover, since u belongs to U, we have that c=0.
This gives
the relation
a-2b=0 => a=2b.

Hence we can take u=(2,1,0).

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question