The following two vectors satisfy the same system of linear equations. u=⎡⎣⎢⎢6−5−5⎤⎦⎥⎥, v=⎡⎣⎢⎢746⎤⎦⎥⎥ Find x and y that make the vector ⎡⎣⎢⎢3xy⎤⎦⎥⎥ a solution to the corresponding homogeneous system:

x=-30/71, y=0

Step-by-step explanation:

if a vector satisfies an equation of the form ax+by+cz=0 then the vector is  

parallel to the plane ax+by+cz=0, and, the cross product of two vectors results in an orthogonal vector to both.

So, <a,b,c> the normal vector of the plane ax+by+cz=0, can be found as the cross product of the two parallel vetors to the plane:

<a,b,c> = <6,-5,-5>×<7,4,6>= <-10,-71,59>

so, the homogeneous system is:

-10x-71y+59z=0

by replacing the vector <3,x,y> in the system

-30-71x+59y=0

So, there are 2 unknown variables and 1 equation, it means that 1 variable is free

so, y=0 is a random defition and x can be obtain with the equation

-30-71x=0 -> x=-30/71

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: