Question

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

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.

Prove that the span of three linearly independent vectors, u, v,
w is R3

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.

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.

Find an example of a nonzero, non-Invertible 2x2 matrix A and a
linearly independent set {V,W} of two, distinct
non-zero vectors in R2 such that
{AV,AW} are distinct, nonzero and
linearly dependent. verify the matrix A in non-invertible, verify
the set {V,W} is linearly independent and verify
the set {AV,AW} is linearly
dependent

3-vectors u, v, and w satisfy u⋅(v ×w)=7. Find [u,v,w]⋅[v×w,
u×w,u×v]^T using properties of the triple scalar product.

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.

Prove this:
Given that V is a linearly dependent set of vectors, show that
there exists a nontrivial linear combination of the vectors of V
that yields the zero vector.

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