College vectors and spaces problems, solved and explained - PlainMath

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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