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ALGEBRA
LINEAR ALGEBRA
VECTORS AND SPACES
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Get help with vectors and spaces
Recent questions in Vectors and spaces
maryam.waleed2020
2022-01-20
If a student selects true or false at random on an examination, assuming independence among answers, determine the probability that: (a) The first correct answer is that of question 3. (b) At most three questions must be answered to obtain the first correct answer.
2022-01-19
On December 26, 2004, a great earthquake occurred off the coast of Sumatra and triggered immense waves (tsunami) that killed some 200,000 people. Satellites observing these waves from space measured 800 km from one wave crest to the next and a period between waves of 1.0 hour. What was the speed of these waves in m/s and in km/h? Does your answer help you understand why the waves caused such devastation?
2022-01-10
3/4x+2=9/10 No decimals
Michael Maggard
2022-01-07
Answered
Write formulas for the unit normal and binormal vectors of a smooth space curve r(t)
Kathleen Rausch
2022-01-07
Answered
Let u and v be distinct vectors of a vector space V. Show that if {u, v} is a basis for V and a and b are nonzero scalars, then both {u+v, au} and {au, bv} are also bases for V.
b2sonicxh
2022-01-07
Answered
Let V, W, and Z be vector spaces, and let
\(\displaystyle{T}:{V}\rightarrow{W}\)
and
\(\displaystyle{U}:{W}\rightarrow{Z}\)
be linear.
If U and T are one-to-one and onto, prove that UT is also
zakinutuzi
2022-01-07
Answered
Let V and W be vector spaces, and let T and U be nonzero linear transformations from V into W. If R(T) ∩ R(U) = {0}, prove that {T, U} is a linearly independent subset of L(V, W).
Tara Alvarado
2022-01-07
Answered
True or False:
4. A vector is a linear combination if u can be written as a sum of scalar multiples of those vectors
5. If
\(\displaystyle{u},{v}\in{V}\)
, then
\(\displaystyle{u}-{v}=-{u}\)
.
6. The objects in a vector space are called vectors.
Jason Yuhas
2022-01-07
Answered
Label the following statements as being true or false.
(a) If V is a vector space and W is a subset of V that is a vector space, then W is a subspace of V.
(b) The empty set is a subspace of every vector space.
(c) If V is a vector space other than the zero vector space {0}, then V contains a subspace W such that W is not equal to V.
(d) The intersection of any two subsets of V is a subspace of V.
(e) An
\(\displaystyle{n}\times{n}\)
diagonal matrix can never have more than n nonzero entries.
(f) The trace of a square matrix is the product of its entries on the diagonal.
interdicoxd
2022-01-06
Answered
Is
\(\displaystyle{\left\lbrace{\left({1},{4},–{6}\right)},{\left({1},{5},{8}\right)},{\left({2},{1},{1}\right)},{\left({0},{1},{0}\right)}\right\rbrace}\)
a linearly independent subset of
\(\displaystyle{R}^{{3}}\)
?
Marenonigt
2022-01-06
Answered
If V is a finite dimensional vector space and W is a subspace, the W is finite dimensional. Prove it.
stop2dance3l
2022-01-06
Answered
Label the following statements as being true or false.
(a) There exists a linear operator T with no T-invariant subspace.
(b) If T is a linear operator on a finite-dimensional vector space V, and W is a T-invariant subspace of V, then the characteristic polynomial of Tw divides the characteristic polynomial of T.
(c) Let T be a linear operator on a finite-dimensional vector space V, and let x and y be elements of V. If W is the T-cyclic subspace generated by x, W' is the T-cyclic subspace generated by y, and W = W', then x y.
Frank Guyton
2022-01-06
Answered
Let W be a subset of the vector space V where u and v are vectors in W. If (
\(\displaystyle{u}\oplus{v}\)
) belongs to W, then W is a subspace of V:
Select one: True or False
rheisf
2022-01-06
Answered
determine whether W is a subspace of the vector space.
\(\displaystyle{W}={\left\lbrace{\left({x},{y}\right)}:{x}-{y}={1}\right\rbrace},{V}={R}^{{2}}\)
Marla Payton
2022-01-05
Answered
What is the connection between vector functions and space curves?
Carol Valentine
2022-01-05
Answered
What is Null Space?
idiopatia0f
2022-01-05
Answered
Let V be a vector space, and let
\(\displaystyle{T}:{V}\rightarrow{V}\)
be linear. Prove that
\(\displaystyle{T}^{{2}}={T}_{{0}}\)
if and only if
\(\displaystyle{R}{\left({T}\right)}\subseteq{N}{\left({T}\right)}.\)
Annette Sabin
2022-01-05
Answered
determine whether W is a subspace of the vector space.
\(\displaystyle{W}={\left\lbrace{f}:{f{{\left({0}\right)}}}=-{1}\right\rbrace},{V}={C}{\left[-{1},{1}\right]}\)
prsategazd
2022-01-05
Answered
Let V, W, and Z be vector spaces, and let
\(\displaystyle{T}:{V}\rightarrow{W}\)
and
\(\displaystyle{U}:{W}\rightarrow{Z}\)
be linear.
If UT is onto, prove that U is onto.Must T also be onto?
dedica66em
2022-01-05
Answered
Let V and W be vector spaces and
\(\displaystyle{T}:{V}\rightarrow{W}\)
be linear. Let
\(\displaystyle{\left\lbrace{y}_{{1}},…,{y}_{{k}}\right\rbrace}\)
be a linearly independent subset of
\(\displaystyle{R}{\left({T}\right)}\)
. If
\(\displaystyle{S}={\left\lbrace{x}_{{1}},…,{x}_{{k}}\right\rbrace}\)
is chosen so that
\(\displaystyle{T}{\left(_\xi\right)}={y}_{{i}}\)
for
\(\displaystyle{i}={1},…,{k}\)
, prove that S is linearly independent.
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