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.
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.
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]