Frank Guyton

2022-01-06

Considering that u and v are vectors in W, let W be a subset of the vector space V. If ($u\oplus v$) belongs to W, then W is a subspace of V:

Select one: True or False

Donald Cheek

Beginner2022-01-07Added 41 answers

Subspace: Suppose that V is a vector space and W is a subset of $V,W\subseteq V$. Give W the same capabilities as V. Then W is a subspace if and only if three conditions are met

- W is non-empty, $W\ne \mathrm{\varnothing}$.

- If $x\in W$ and $y\in W$, then $x+y\in W$.

- If $\alpha \in R$ and $x\in W$, then $\alpha x\in W$.

The given statement is, Let W be a subset of the vector space V where u and v are vectors in W. If (u+v) belongs to W, then W is a subspace of V. Since the remaining two conditions are not satisfied, therefore the given statement is False.

An object moving in the xy-plane is acted on by a conservative force described by the potential energy function

where$U(x,y)=\alpha (\frac{1}{{x}^{2}}+\frac{1}{{y}^{2}})$ is a positive constant. Derivative an expression for the force expressed terms of the unit vectors$\alpha$ and$\overrightarrow{i}$ .$\overrightarrow{j}$ I need to find a unique description of Nul A, namely by listing the vectors that measure the null space

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$A=\left[\begin{array}{ccccc}1& 5& -4& -3& 1\\ 0& 1& -2& 1& 0\\ 0& 0& 0& 0& 0\end{array}\right]$T must be a linear transformation, we assume. Can u find the T standard matrix.$T:{\mathbb{R}}^{2}\to {\mathbb{R}}^{4},T\left({e}_{1}\right)=(3,1,3,1)\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}T\left({e}_{2}\right)=(-5,2,0,0),\text{}where\text{}{e}_{1}=(1,0)\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}{e}_{2}=(0,1)$

?Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR

Consider the points below

P(1,0,1) , Q(-2,1,4) , R(7,2,7).

a) Find a nonzero vector orthogonal to the plane through the points P,Q and R.

b) Find the area of the triangle PQR.Consider two vectors A=3i - 1j and B = - i - 5j, how do you calculate A - B?

Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate 2A-3(B-C)?

What is the projection of $<6,5,3>$ onto $<2,-1,8>$?

What is the dot product of $<1,-4,5>$ and $<-5,7,3>$?

Which of the following is not a vector quantity?

A)Weight;

B)Nuclear spin;

C)Momentum;

D)Potential energyHow to find all unit vectors normal to the plane which contains the points $(0,1,1),(1,-1,0)$, and $(1,0,2)$?

What is a rank $1$ matrix?

How to find unit vector perpendicular to plane: 6x-2y+3z+8=0?

Can we say that a zero matrix is invertible?

How do I find the sum of three vectors?

How do I find the vertical component of a vector?