Question is included in the attached picture. How do I go about finding [T]b under the standard basis? I don't know where to start because I'm unfamiliar with the notation. I believe 2p'(t) means the derivative of p'(t)^2.

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- Apr 14th 2013, 03:59 PMlamentofkingFind the B-Matrix of T under the standard basis.
Question is included in the attached picture. How do I go about finding [T]b under the standard basis? I don't know where to start because I'm unfamiliar with the notation. I believe 2p'(t) means the derivative of p'(t)^2.

- Apr 15th 2013, 07:22 AMmathguy25Re: Find the B-Matrix of T under the standard basis.
If I'm understanding this correctly (I too do not understand the notation used here but I have solved similar problems).

Let A = {1, x, x^2} be our standard basis in P^2.

Then T(A) = {T(1), T(t), T(t^2)} = {2*0 - 3*1, 2*1 - 3*t, 2*2t - 3*t^2} = {-3, 2-3t, 4t-3t^2} = {-3 + 0t + 0t^2, 2 - 3t + 0t^2, 0 + 4t - 3t^2}

Then matrix = [-3; 2; 0]

.....................[0; -3; 4]

.....................[0; 0; -3]