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Linear Algebra mixed with Calculus
Let T: P^2>R^3 be the linear transformation given by T(p(x)) = <p(3), p(5), p'(2)>, B={1,x, x^2} the standard basis for P^2 and B' = {e1, e2, e3} be the standard basis for R^3.
Use the inverse of the matrix [T]_B,B' to find a quadratic polynomial passing through (3, 75) and (5, 99) and whose tangent line at x=2 has a slope of 13.
 one year ago
 one year ago
Linear Algebra mixed with Calculus Let T: P^2>R^3 be the linear transformation given by T(p(x)) = <p(3), p(5), p'(2)>, B={1,x, x^2} the standard basis for P^2 and B' = {e1, e2, e3} be the standard basis for R^3. Use the inverse of the matrix [T]_B,B' to find a quadratic polynomial passing through (3, 75) and (5, 99) and whose tangent line at x=2 has a slope of 13.
 one year ago
 one year ago

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mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352007689346:dw
 one year ago

roadjesterBest ResponseYou've already chosen the best response.0
uhh, wouldn't adding the three elementary matricies, and taking the rref, give you the inverse? I just don't know where to go from there
 one year ago

roadjesterBest ResponseYou've already chosen the best response.0
ok, no idea what you're writing, but the numbers come out to be the same inverse that I got after doing the GaussJordan Algorithm But a little English would be nice. If we don't interact, I have no clue what you're writing
 one year ago

roadjesterBest ResponseYou've already chosen the best response.0
I take that back, the numbers are a little different
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
I have just compute the inverse matrix with an individual method. Now we should follow the second part.
 one year ago

roadjesterBest ResponseYou've already chosen the best response.0
dw:1352008344540:dw
 one year ago

roadjesterBest ResponseYou've already chosen the best response.0
By adding these three columns: 1 0 0 0 1 0 0 0 1 to my original matrix and row reducing, I get that matrix as my inverse. I'm unfamiliar with your technique.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352008523111:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352008571359:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352008680377:dw
 one year ago

roadjesterBest ResponseYou've already chosen the best response.0
While you have good intentions, just writing the answer with no explanation does me no good since I not only do not learn anything, but I do not know what you are doing. Could you please slow down to explain? Also, just writing out the solution is against the CoC.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352008780107:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
Don't attend to inverse matrix. Just follow the second part. suppose I got it.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352009050198:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352009161620:dw
 one year ago

PreethaBest ResponseYou've already chosen the best response.0
I think Mahmit is being really painstaking in trying to explain this. Good work.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352009295173:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
Very nice question. I was really enjoyed. And I hope you could understand it.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
I try to give you the same one.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352009879051:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352010149750:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
I always thought how a software can find the polynomial with passing some points and some particular slope. So I figure it out. Thank you.
 one year ago

roadjesterBest ResponseYou've already chosen the best response.0
Umm, sure, although don't you think writing an actual program, the language (C++, Java, D, Ruby, Python, etc) doesn't matter, would be easier than doing this by hand every time?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
I must find out some polynomial for a control system online. I have information with y, y' y'',... y(n). This problem help me a lot.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.3
dw:1352010808815:dw
 one year ago

helder_edwinBest ResponseYou've already chosen the best response.0
Indeed. very interesting.
 one year ago
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