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anonymous
 5 years ago
if a1=(7,1,4) a2=(4,0,1) and a3=(3,5,0) and the set S={a1,a2,a3} is a basis for R3, how do you find the equation y=2a13a2+a3 (ps that is the answer, I just don't know how to get to it)
anonymous
 5 years ago
if a1=(7,1,4) a2=(4,0,1) and a3=(3,5,0) and the set S={a1,a2,a3} is a basis for R3, how do you find the equation y=2a13a2+a3 (ps that is the answer, I just don't know how to get to it)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0trying to find the linear combination y, they give the answer but they dont explain how they got to it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0perhaps I am reading this wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know the coordinates of y?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0didnt think it was part of it, but they did mention that a little before

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, that is the important bit. a1(x,y,z) = (7,1,4) a2(x,y,z) = (4,0,1) and a3(x,y,z) = (3,5,0)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, so how do we find the linear combination?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so a linear combination of the xcoordinates of a1,a2,a3 should give the x coordinate of y, a linear combination of the ycoordinates of a1,a2,a3 should give the y coordinate of y, a linear combination of the zcoordinates of a1,a2,a3 should give the z coordinate of y.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so 7m+4n3p=1 m+5p=3 and4m+n = 5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ahh ok thanks a lot, then solve the matrix from there eh?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.03 equations, 3 unknowns, solve to get m,n,p those will be the coefficients of the equation y = ma1+na2+pa3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just one more thing....what did we do here? we had a coordinate, then we established the basis, and found another coordinate

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0did we change it from cartesian?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no its in Cartesian coordinates only. all we did was to find a linear combination of the three points which gives the point y.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it follows that [y]s=(2,3,1) in the text, this isn't a coordinate?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no, those are the coefficients of the linear combination.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i gotta run, hope that helped!
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