Question

Prove that the span of three linearly independent vectors, u, v,
w is R^{3}

Answer #1

Let u, vand w be linearly dependent vectors in a vector space V.
Prove that for any vector z in V whatsoever, the vectors u, v, w
and z are linearly dependent.

Let (u,v,w,t) be a linearly independent list of vectors in R4.
Determine if (u, v-u, w+5v, t) is a linearly independent list.
Explain your reasoning and Show work.

Let S={u,v,w}S={u,v,w} be a linearly independent set in a vector
space V. Prove that the set S′={3u−w,v+w,−2w}S′={3u−w,v+w,−2w} is
also a linearly independent set in V.

vectors u=(1,2,3), v=(2,5,7), w=(1,3,5) are linearly dependent
or independent? (using echelon form)

4. Prove the Following:
a. Prove that if V is a vector space with subspace W ⊂ V, and if
U ⊂ W is a subspace of the vector space W, then U is also a
subspace of V
b. Given span of a finite collection of vectors {v1, . . . , vn}
⊂ V as follows:
Span(v1, . . . , vn) := {a1v1 + · · · + anvn : ai are scalars in
the scalar field}...

determine the span of u=(1,2,0) v=(3,2,-1) w=(-2,0,1) and determine
if u,v, and w are linearly dependent.

Suppose v1, v2, . . . , vn is linearly independent in V and w ∈
V . Show that v1, v2, . . . , vn, w is linearly independent if and
only if w ∈/ Span(v1, v2, . . . , vn).

Find a linearly independent set of vectors that spans the same
subspace of R3 as that spanned by the vectors
[-3,1,3] , [-6,5,5],[0,-3,1]
Linearly independent set:
[x,y,z] , [x,y,z]

If v1 and v2 are linearly independent vectors in vector space V,
and u1, u2, and u3 are each a linear combination of them, prove
that {u1, u2, u3} is linearly dependent.
Do NOT use the theorem which states, " If S = { v 1 , v 2 , . . . ,
v n } is a basis for a vector space V, then every set
containing
more than n vectors in V is linearly dependent."
Prove without...

In
3 dimensions, draw vectors u, v, w, and x such that u+v+w=x. The
vectors u and x share an initium. You may pick the size of your
vectors. Make sure the math works.
Find the angle between vector x and vector u.

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