Boost Your Knowledge with Vectors Explanation

College
Algebra
Linear algebra
Vectors and spaces

Let $\vec{v_{1}} = [\begin{matrix} 2 \\ 3 \end{matrix}]$ and $\vec{v_{1}} = [\begin{matrix} 4 \\ 6 \end{matrix}]$ what is the span of the vector space defined by $\vec{v_{1}}$ and $\vec{v_{1}}$ ? Explain your answer in detail?

Lainey Goodwin 2022-01-24

Geometrically, the span of two non-parallel vectors in $R^{3}$ is?
1) one octant
2) a line
3) a point
4) the whole 3-space
5) a plane

Branden Valentine 2022-01-24

What are the standard three-dimensional unit vectors?

m4tx45w 2022-01-24

Suppose there was a basis for and a certain number of dimensions for subspace W in $R^{4}$ .Why is the number of dimensions 2?
$W = {⟨ 4 s - t, s, t, s ⟩ ∣ s, t \in R}$
For instance, apparently, ${⟨ 0, 1, 4, 1 ⟩, ⟨ 1, 1, 3, 1 ⟩}$
is a valid set, and it happens to be of dimension 2 in $R^{4}$ . Does a basis for $R^{n}$ have to have n vectors?

David Rojas 2022-01-24

Let $V = R^{3}$ and $W = {(x, y, z) ∣ x, y, z \in Q}$ . Is $W \leq V$ ? Justify your answer.
So, I wrote:
1) $(0, 0, 0) \in W$
2) $α, β \in W$
$α = (x, y, z), β = (x^{'}, y^{'}, z^{'})$
$α, β = (x + x^{'}, y + y^{'}, z + z^{'}$ so $α + β \in W$
3) $c \in R, α \in W$
$α = (x, y, z)$
$c α = (c x, c y, c z)$ so $c α \in W$
Hence, $W \leq V$

maliaseth0 2022-01-24

How could I determine whether vectors $P < - 2, 7, 4 >, Q < - 4, 8, 1 >, and R < 0, 6, 7 >$ are all in the same plane?

maliaseth0 2022-01-24

What is the magnitude of vector $A B$ if $A = (4, 2, - 6)$ and $B = (9, - 1, 3)$ ?

jelentetvq 2022-01-24

How do I find the unit vector for $v = < 2, - 5, 6 >$

licencegpopc 2022-01-24

Let $V = S p a n {f_{1}, f_{2}, f_{3}}$ , where $f_{1} = 1, f_{2} = e^{x}, f_{3} = x e^{x}$
a) Prove that $S = {f_{1}, f_{2}, f_{3}}$ is a basis of V. b) Find the coordinates of $g = 3 + (1 + 2 x) e^{x}$ with respect to S. c) Is ${f_{1}, f_{2}, f_{3}}$ linearly independent?

Fiona Petersen 2022-01-23

Let V be a vector space over F. Explain why we can think of V as a vector space over K ( K subset of F)?

estadsocm3 2022-01-23

How do I find the angle between two vectors in three-dimensional space?

Swebaceacichegh 2022-01-23

How do you find the inner product and state whether the vectors are perpendicular given $< 8, 4 > \cdot < 2, 4 >$

Haialarmz6 2022-01-22

How do you determine if the vectors are coplanar: a = [-2,-1,4], b = [5,-2,5], and c = [3,0,-1]?

Trace Cline 2022-01-22

Which of the following statements are true/false?Justify your answer.
(i) $R^{2}$ has infinitely many non-zero, proper vector subspaces.
(ii) Every system of homogeneous linear equations has a non zero solution.

licencegpopc 2022-01-22

How do you find the equation of the plane in xyz-space through the p=(4,5,4) and perpendicular to the n=(−5,−3,−4)?

treslagosnv 2022-01-22

Is there an infinite dimensional vector space H with bounded linear operator from H onto H which preserves the inner product?

Alisha Pitts 2022-01-22

What is the span of a matrix?

poveli1e 2022-01-21

Which vectors define the complex number plane?

Aaden Lam 2022-01-21

For what value of $λ$ the following vectors will form a basis for $E^{3}$ .
$a_{1} = (1, 5, 3), a_{2} = (4, 0, λ), a_{3} = (1, 0, 0)$ ?

Gavin Frye 2022-01-21

How do vectors represent a point in space?

One of the most fascinating parts of linear algebra is dealing with the vectors and vector spaces. You can start with the equations or examine the solutions that have already been provided to the most common questions. Since these are mostly the same, you will find sufficient help as you try to challenge your homework duties. Remember to use scalars and check your objects accurately. We also provide vectors math help by offering various solutions based on Physics or specific engineering problems. Make sure that you browse through the available posts and seek something that sounds similar to your task.

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