w.u1=0
w.u2=0
..
w.ur=0
they are all orthogonal to each other.
=k1(w.u1) + k2(w.u2) + ... + kr(w.ur)
=k1(0) +k2(0) +...+ kr(0)
=0
and btw man i really appreciate u walkin me through this proof. This helps me sooo much for this proof and just solving proofs in general.
Compute (k1u1+k2u2+...+krur).w
=w.k1u1 + w.k2u2 + ... + w.krur
=k1(w.u1) + k2(w.u2) + ... + kr(w.ur)
sorry about bein really dumb with this, I am horrible with proofs. but good with numbers...
i am sooo confused.
b and w are both vectors.
so b=(b1,b2,...br)
w=(w1,w2,...wr) w vector is perpendicular to b vector (b lies in the span of u1,u2,...ur)
so b1w1+b2w2+...+brwr=0
*i noticed u edited what u asked me.
What is (k1u1+k2u2+...+krur).w?
k1u1w1+k2u2w2+...+krurwr = 0...
So w has to be orthogonal to all of the vectors in the span{u1,u2,...,ur}
k1u1+k2u2+...+krur=b to test for spanning where b is an arbitrary vector.
would 'b' be w in this case?
Homework Statement
Let V be the inner product space. Show that if w is orthogonal to each of the vectors u1, u2,...,ur, then it is orthogonal to every vector in the span{u1,u2,...,ur}.
Homework Equations
u.v=0 to be orthogonal
If u and v are vectors in an inner product space, then...
u and v are contained in V
Lets say the scalar multiplication is defined as:
ex.
ku=k^2 u or ku = (0,ku2) u=(u1,u2)
does this mean that this is also the same for different scalar m?
mu=m^2 u or mu = (0,mu2) u=(u1,u2)
and does this mean the same for any vector v
kv=k^2 v or...
so u guys know and I am not confusing you guys i showed 2 examples there to help show my problem.
Ex 1.
Lets say the scalar multiplication is defined as:
ku = (0,ku2) u=(u1,u2)
does this then mean that this is also the same for different scalar m?
mu = (0,mu2) u=(u1,u2)
and...
u and v are contained in V
Lets say the scalar multiplication is defined as:
ex.
ku=k^2 u or ku = (0,ku2) u=(u1,u2)
does this mean that this is also the same for different scalar m?
mu=m^2 u or mu = (0,mu2) u=(u1,u2)
and does this mean the same for any...
Homework Statement
I have a few homework questions that ask for the direction of induced current for ex a loop of wire.
I can't figure out how to find it .
Homework Statement
A 25pF parallel plate capacitor with an air gap b/w the plates is connected to a 100v battery. A Teflon slab is then inserted b/w the plates and completely fills the gap. What is the change in charge on the positive plate when the Teflon is inserted?
Homework Equations...