beljuA

2021-03-11

Find all scalars ${c}_{1},{c}_{2},{c}_{3}$ such that ${c}_{1}(1,-1,0)+{c}_{2}(4,5,1)+{c}_{3}(0,1,5)=(3,2,-19)$

Nathanael Webber

Skilled2021-03-12Added 117 answers

The equation ${c}_{1}(1,-1,0)+{c}_{2}(4,5,1)+{c}_{3}(0,1,5)=(3,2,-19)$

becomes$({c}_{1}-{c}_{1},0)+(4{c}_{2},5{c}_{2},{c}_{2})+(0,{c}_{3}5{c}_{3})=(3,2,-19)$

which can be written as$({c}_{1}+4{c}_{2},-c2+5{c}_{2}+{c}_{3},{c}_{2}+5{c}_{3})=(3,2,-19)$

This gives us the the system${c}_{1}+4{c}_{2}=3$

$-{c}_{1}+5{c}_{2}={c}_{3}=2$

${c}_{2}+5{c}_{3}=-19$

From the first equation we get${c}_{1}=3-4{c}_{2}$

From the third equation we get${c}_{2}=-19-5{c}_{3}$

Thus,${c}_{1}=3-4{c}_{2}=3-4(-19-5{c}_{3})+{c}_{3}=2\Rightarrow -44{c}_{3}-174=2$

This yields$-44{c}_{3}=176\Rightarrow {c}_{3}=-4$

Thus,${c}_{2}=-19-5{c}_{3}=-19-5\cdot (-4)\Rightarrow {c}_{2}=1$

and${c}_{2}=79+20{c}_{3}=79+20\cdot (-4)\Rightarrow {c}_{1}=-1$

Therefore, to conclusude,${c}_{1}=-1,{c}_{2}=1,{c}_{3}=-4$

becomes

which can be written as

This gives us the the system

From the first equation we get

From the third equation we get

Thus,

This yields

Thus,

and

Therefore, to conclusude,

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.

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?