Co-ordinate transformation matrix

asif zaidi

Plz advise if my approach is correct for 1st part and for 2nd part, I need some help.


Problem Statement
Consider the linear transformation T: R3->R2 whose matrix with respect to standard bases is given by | 2,1,6 |
| 0,2,-1|.
Now consider the bases f1={2,4,0}, f2={1,0,1}, f3 = {0,3,0} in R3 and
g1 = {1,1} and g2 = {1,-1}

Compute the coordinate transformation matrices between the standard bases and these bases and compute the matrix of T with respect to the new bases

Problem solution

For first part, I am doing the following
Express u1, u2, u3 in terms of standard bases vectors
u1 = 2e1 + 4e2;
u2 = e1 + e3;
u3 = 3e2;
Solve for e1,e2,e3 in terms of u1, u2, u3 and transpose of this is my co-ordinate transformation matrix. Is this correct?

For g vectors, do in a similar manner

For second part
I don't understand this part. How do I compute the matrix of T wrt these new bases. Any pointers would be appreciated.

FunkyDwarf

Look where T takes the new standard basis elements ie equiv of (1,0,0), (0,1,0) etc

asif zaidi

Don't really understand your response. Could you elaborate plz.

Also, is my 1st part to solution correct?

Thanks

radou

Look at how exactly the matrix representation of an operator is given.