Question

Chaning coordinates Linear Algebra 2 question

Answer 1

I found (ST) but I don't know how to find the ME<-B or MD<-E

Answer 2

sorry, i am not familiar with the notation \(M_{E\leftarrow B}(T)\)

Answer 3

does it mean the matrix of T with respect to the bases B and E?

Answer 4

Um I think so, I'm not good with putting math into words lol

Answer 5

wait I might have something hold on

Answer 6

ok. but shouldn't u have the meaning of this in your notes or your book?

Answer 7

If E is in basis R5 would that be \[\left[\begin{matrix}1&0&0&0&0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&1\end{matrix}\right]\]

Answer 8

i don't have much time. so I think this is like this:
u have \(T:V\to W\) a linear transformation with B and C the basis of V and W, respectively.

Answer 9

let's say \(B=\{b_1,\dots,b_n\}\) and \(C=\{c_1,\dots,c_m\}\) then first u compute
\[ T(b_i)\qquad i=1,\dots,n \]
then u solve the linear systems
\[ \large T(b_i)=\alpha_{1i}c_1+\alpha_{2i}c_2+\dots+\alpha_{mi}c_m \]
the solution of each of these systems will give the columns of the matrix

Answer 10

let's find \(M_{E\leftarrow B}(T)\)
first compute
\[ T(v_1)=T(1,-2)=(-2,1-2,-1,3) \]
right?

Answer 11

\[ T(v_2)=T(-3,4)=(4,-3,4,1,-7) \]

Answer 12

there is one comma between 1 and -2 missing

Answer 13

I actually used the equation (ME<-E(id)^-1) (ME<-E(T)) (ME<-B(id))

Answer 14

what equation?

Answer 15

you basically times each given matrix

Answer 16

I think I got it now though so thank you

Answer 17

ok. i have to go, but I'll be back in a couple of hours, in case you need more help