Find the transition matrix from B to B'.B = {(1, 0), (0, 1)}, B' = {(2, 16), (1, 9)}
Question
Find the transition matrix from B to B'.
Let
B = {(1, 0), (0, 1)}
B' = {(2, 16), (1, 9)}
Determine the transition matrix from the basis B to the basis B'.
Solution
To find the transition matrix from B to B', we need to express each vector in B' as a linear combination of the vectors in B.
The vectors in B are (1, 0) and (0, 1).
The vectors in B' are (2, 16) and (1, 9).
We can express (2, 16) as 2*(1, 0) + 16*(0, 1) and (1, 9) as 1*(1, 0) + 9*(0, 1).
So, the transition matrix from B to B' is
| 2 1 |
|16 9 |
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