may i know, given that A is the basis of (a1,a1,a) , B is the basis of )b1,b2,b3)
is
b1=a1-a3
b2=a1-a2
b3=a1+a1+a3
the transitition matrix from A to B or from B to A? i thought this was the transition matrix from A to B but the answers in my notes seems to suggest otherwise
sorry it was a typo on my part. its b3= a1+ a2+ a3
in such a case,
b1=a1-a3
b2=a1-a2
b3=a1+a2+a3 is the transition matrix from basis A to B right?
let this set of equations above be P.
in this question, i was also given that T is the linear map whose matrix in basis A is
(3 4 5 )
(0 1 -3)
(2 -1 -2)..let me denote this matrix as A
then isit right for me to say that
T(b)=P A P^-1 v(b)
where T(b) is the matrix of T in B and v(b) is the vector in B..
thank you!