, 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.

- roadjester

Linear Algebra mixed with Calculus
Let T: P^2-->R^3 be the linear transformation given by T(p(x)) =

, 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.

- jamiebookeater

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- anonymous

|dw:1352007689346:dw|

- roadjester

ok, HUH???

- roadjester

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

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## More answers

- roadjester

ok, no idea what you're writing, but the numbers come out to be the same inverse that I got after doing the Gauss-Jordan Algorithm
But a little English would be nice. If we don't interact, I have no clue what you're writing

- anonymous

Now second part !

- roadjester

I take that back, the numbers are a little different

- anonymous

I have just compute the inverse matrix with an individual method.
Now we should follow the second part.

- roadjester

|dw:1352008344540:dw|

- roadjester

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.

- anonymous

|dw:1352008523111:dw|

- anonymous

|dw:1352008571359:dw|

- roadjester

MAHMIT!!!

- anonymous

|dw:1352008680377:dw|

- roadjester

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.

- anonymous

|dw:1352008780107:dw|

- anonymous

Don't attend to inverse matrix.
Just follow the second part.
suppose I got it.

- anonymous

|dw:1352009050198:dw|

- anonymous

|dw:1352009161620:dw|

- anonymous

Is it clear?

- Preetha

I think Mahmit is being really painstaking in trying to explain this. Good work.

- anonymous

|dw:1352009295173:dw|

- anonymous

Very nice question. I was really enjoyed. And I hope you could understand it.

- roadjester

Erm, thanks.

- anonymous

I try to give you the same one.

- anonymous

|dw:1352009879051:dw|

- anonymous

|dw:1352010149750:dw|

- anonymous

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.

- roadjester

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?

- anonymous

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.

- anonymous

|dw:1352010808815:dw|

- helder_edwin

Indeed. very interesting.

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