Find the transition matrix from B to B'.B = {(1, 0), (0, 1)}, B' = {(2, 16), (1, 9)}

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 |

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).

1. Express (2, 16) as a linear combination of (1, 0) and (0, 1):

   We can see that (2, 16) = 2*(1, 0) + 16*(0, 1). So, the first column of the transition matrix is (2, 16).

2. Express (1, 9) as a linear combination of (1, 0) and (0, 1):

   Similarly, (1, 9) = 1*(1, 0) + 9*(0, 1). So, the second column of the transition matrix is (1, 9).

Therefore, the transition matrix from B to B' is:

| 2 1 |
|16 9 |