OK, I'm a little confused about this.
We have vector spaces , with bases and . We then have a matrix
The matrix isn't working in the Latex editor, so let's just go on.
OK.
Tell me everything you know about vector space bases.
Let A and B be vector spaces, (which turn out to be real btw) that have ordered bases alpha=(a1,a2,a3) and beta = (b1,b2,b3,b4). The matrix T: A->B is: 2 9 7 4 5 7 9 4 3 2 8 3 work out the alpha coord of a1+a2+a3 and hence or otherwise find T(a1+a2+a3) relative to b1,b2,b3,b4
Well since your and in terms of co-efficients translates to , finding amounts to computing
Finally this will give you a 4 x 1 vector. These are the coefficients of b_1,b_2,b_3,b_4 in the linear combination of the vector in that order.
Hey bleesdan,
Use \begin{pmatrix}2 & 9 & 7\\4 & 5 & 7\\9 & 4 & 3\\2 & 8 & 3\end{pmatrix} to get
Thanks for your help, i have further questions; its most whats being asked of me that I cant figure.
Ive been asked to write down the change matrix been beta to alpha. Where beta is: (4i+6j, 7i+2j, 3i+5j+9k) and alpha has the standard basis. Am I just being stupid and the change matrix is?
4 6 0
7 2 0
3 5 9
or do I need to do something to it? or?
next part is find the matrix which represents
4 5 6
7 3 5
3 5 8
relative to beta
correct. Well done.Ive been asked to write down the change matrix been beta to alpha. Where beta is: (4i+6j, 7i+2j, 3i+5j+9k) and alpha has the standard basis. Am I just being stupid and the change matrix is?
4 6 0
7 2 0
3 5 9
I'm not sure what this part is asking, sorry.next part is find the matrix which represents
4 5 6
7 3 5
3 5 8
relative to beta