- #1
schmiggy
- 38
- 0
Homework Statement
Let V be the vector space of all symmetric 2x2 matrices, and consider the bases.
S = {
[1 0] [0 1] [0 0]
[0 0],[1 0],[0 1]}
B = {
[1 1] [-1 1] [1 0]
[1 2],[ 1 1],[0 1]}
of V.
Find the transition matrix Ps,b. Use your answer to calculate Pb,s.
Homework Equations
a = [itex]\alpha[/itex][itex]_{1}[/itex]b[itex]_{1}[/itex] + [itex]\alpha[/itex][itex]_{2}[/itex]b[itex]_{2}[/itex] + [itex]\alpha[/itex][itex]_{3}[/itex]b[itex]_{3}[/itex] +... + [itex]\alpha[/itex][itex]_{k}[/itex]b[itex]_{k}[/itex]
The Attempt at a Solution
I honestly don't know where to start. All previous questions like this we've dealt with vectors and not 2x2 matrices..
ie B = (1,3),(2,1)
(1,3) = 1(1,0) + 3(0,1) and (2,1) = 2(1,0) + 1(0,1)
So Ps,b = [1 2] and Pb,s is just the inverse of Ps,b = -1/5[1 -2]
[3 1] [-3 1]
But I don't know how to even start when I'm given 2x2 matrices..