1. ## transition

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

2. Originally Posted by alexandrabel90
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
??? Well, that's NOT a matrix, it is a system of equations. What matrix did you mean?

3. im trying to solve for the matrix of T in basis B.

i was given that A is the basis of (a1,a1,a) , B is the basis of )b1,b2,b3)
and this set of equations
b1=a1-a3
b2=a1-a2
b3=a1+a1+a3.

4. Originally Posted by alexandrabel90
im trying to solve for the matrix of T in basis B.

i was given that A is the basis of (a1,a1,a) , B is the basis of )b1,b2,b3)
and this set of equations
b1=a1-a3
b2=a1-a2
b3=a1+a1+a3.
Are you sure of that last equation? b3= 2a1+ a3?

Then $\begin{bmatrix}b_1 \\ b_2 \\ b_3\end{bmatrix}= \begin{bmatrix}1 & 0 & -1 \\ 1 & -1 & 0 \\ 2 & 0 & 1\end{bmatrix}\begin{bmatrix}a_1 \\ a_2 \\ a_3\end{bmatrix}$

or b3= a1+ a2+ a3?

Then $\begin{bmatrix}b_1 \\ b_2 \\ b_3\end{bmatrix}= \begin{bmatrix}1 & 0 & -1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{bmatrix}\begin{bmatrix}a_1 \\ a_2 \\ a_3\end{bmatrix}$

5. 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!

6. what im unsure about is that usually, for the questions on these chapters that i have done, the formula that i use is

T(B) =P^-1 A P v(B)..but in this case, it seems to be the other way round..did i maake a mistake somewhere in my workings?