Question

What does it mean if a set of basis vectors is complete?

a. The only vector that is orthogonal to every basis vector is the 0 vector

b. The inner product of any two basis vectors is 0

I was thinking it was B but how would it be justified

Answer #1

A2. Let v be a fixed vector in an inner product space V. Let W
be the subset of V consisting of all vectors in V that are
orthogonal to v. In set language, W = { w LaTeX: \in
∈V: <w, v> = 0}. Show that W is a subspace of V. Then,
if V = R3, v = (1, 1, 1), and the inner product is the usual dot
product, find a basis for W.

Which of the four fundamental subspaces are orthogonal? What
does this mean about the vectors that live in those subspaces? If
Ax = b and Ay =
0, where do each of the vectors,
x, b, and y,
live?

Let V be a vector space of dimension n > 0, show that
(a) Any set of n linearly independent vectors in V forms a
basis.
(b) Any set of n vectors that span V forms a basis.

Problem 6.4 What does it mean to say that a set of vectors {v1,
v2, . . . , vn} is linearly dependent? Given the following vectors
show that {v1, v2, v3, v4} is linearly dependent. Is it possible to
express v4 as a linear combination of the other vectors? If so, do
this. If not, explain why not. What about the vector v3? Anthony,
Martin. Linear Algebra: Concepts and Methods (p. 206). Cambridge
University Press. Kindle Edition.

The cross product of 2 vectors, A and B, gives a
vector C that is perpendicular to the plane AB. But we can't always
contain two vectors in a plane (so we can't always find a plane AB) right?
Would the cross product be valid in this case? What would be the
result of the cross product?
Thanks in advance

Two 3D vectors, A and B , are represented in terms of the
Cartesian basis unit vectors, i , j , k as follows:
A=2i-3j+k
B=10i+9j-4k
1) plot A and B in a Cartesian coordinate system
2) calculate A + B
3) calculate A · B using the scalar product formula
4) calculate the magnitudes of A and B
5) calculate the angle between A and B
6) calculate A x B using the determinant formula
7) show that the...

please answer all of them; only need final answer
h. The length of the vector c = (2, -3, 1) is?
i. If |r| = 4, then the value of |-5r| is?
j. The cross product of vectors a = (-1, 4, 6) and b = (3, 0, 2)
is?
k. The vectors v = (3, 4) is projected onto the x-axis The
length of the projection is?
l. Rounded to the nearest integer, a two-dimensional vector with
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1) Your colleague on the skyscraper design team brings in a
quiver (a set) full of
vectors. She would like to know which ones could be used as a
basis. Select vectors from the
quiver that will span the subspace represented by all vectors in
the quiver.
Quiver Set: v1 = (1,−1,5,2), v2 = (−2,3,1,0), v3 = (4,−5,9,4),
v4 = (0,4,2,−3), v5 =(−7,18,2,−8)
Part 2: She wants to know if they span R6. What is the problem
with her question?...

Linear Algebra
What does it mean for vectors to span Rm? Please give
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There is 6-31G(d) in Chemistry basis set.
What does 6,3,1,G,d mean for each?

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