2022-05-05

Suppose$U=\{(x,y,x+y,x-y,2x)\in {F}^{5},x,y\in F\}$ . Find a subspace $W$of ${F}^{5}$ such that ${F}^{5}=U\oplus W$.

xleb123

Skilled2023-05-04Added 181 answers

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?

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B)Nuclear spin;

C)Momentum;

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