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nasha1234
consider the bases B=[u1,u2] and B'[v1,v2] for R^2, where u1=[1 0], u2 [0 1], v1=[2 1], v2=[-3 4]. its matrix 1x2. how to find the transition matrix from B' to B and the other way around? also, compute the coordinate vector [w]b where w=[3 -5] and use (9) to compute [w]b'
hey, friend, we have formula to find the transition matrix from b' to B. B is the new place you want to come there, so put B first in |B|B'| and make them become | I | some new matrix| . the last "some new matrix" is matrix transition from B' to B, denoted by P_(B' to B) and if you want to have the matrix transition from B to B', just take P inverse. To compute [W]_B , you must do something like W = C1*u1 + C2 * u2 = (3,-5) (actually, it's not hard , hopefully you know how to get this) after have [w]B, use inverse transition matrix to calculate [W}B' by putting into the formula P^- * [W]B hopefully you understand my English