Holly Guerrero

2022-01-04

Problem 2:

If$V={R}^{3}$ is a vector space and let H be a subset of V and is defined as $H=\{(a,b,c):{c}^{2}+{b}^{2}=0,a\ge 0\}$ . Show that H is not subspace of vector space

Problem 3

Let$V={R}^{3}$ be a vector space and let W be a subset of V, where $W=\{(a,b,c):{a}^{2}={b}^{2}\}$ . Determine whether W is a subspace of vector space or not.

If

Problem 3

Let

braodagxj

Beginner2022-01-05Added 38 answers

Problem 2:

$V={R}^{3}$

$H=\{(a,b,c):{c}^{2}+{b}^{2}=0,a\ge 0\}$

At$x=(1,0,0)\in H$

But$\alpha =-2$ is scalar in R

$\alpha x=(-2)(1,0,0)$

$=(-2,0,0)\notin H(-2<0)$

Not subspace of vector space V

At

But

Not subspace of vector space V

Piosellisf

Beginner2022-01-06Added 40 answers

Problem 3:

$V={R}^{3}$

$W=\{(a,b,c):{a}^{2}={b}^{2}\}$

At$x(1,-1,0)\in H$

At$y(1,1,0)\in H$

But$x+y=(2,0,0)\notin H$

$\therefore {2}^{2}\ne {0}^{2}$

Not subspace of vector space V

At

At

But

Not subspace of vector space V

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

?

$A=\left[\begin{array}{ccccc}1& 5& -4& -3& 1\\ 0& 1& -2& 1& 0\\ 0& 0& 0& 0& 0\end{array}\right]$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.

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C)Momentum;

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