A1 + a3 + A5 + A7 = 4, find A2 + A4 + A6

The question is like this
If {an} is known to be an arithmetic sequence and a1 + a3 + A5 + A7 = 6, then A2 + A4 + A6 is equal to
Then a1 + A7 = A3 + A5 = A2 + A6 = 2a4
Because a1 + A2 + a3 + A4 = 7, so 4a4 = 4, so A4 = 1
So A2 + A4 + A6 = 3A4 = 3

Given that A1, A2, A3 are the bases of R3, a = a1 + A2 + a3, find the transition matrix from A1, A2, A3 to a1 + A2, A2 + a3, A3 + A1,
And find the coordinates of a under the new basis

(a 1 + a 2, a 2 + a 3, a 3 + a 1) = (a 1, a 2, a 3) PP = 1011 0011 P is the transition matrix

On the problem of finding the transition matrix from base a to base B (B1, B2, B3) = (A1, A2, A3) C
I know (A1, A2, A3 | B1, B2, B3) = (E | C)
If it is (B1, B2, B3 | A1, A2, A3) = (E | what)?

From (B1, B2, B3) = (A1, A2, A3) C
We get (A1, A2, A3) ^ - 1 (B1, B2, B3) = C
So (A1, A2, A3 | B1, B2, B3) = (E | C)
And (B1, B2, B3 | A1, A2, A3) = (E, (B1, B2, B3) ^ - 1 (A1, A2, A3)) = (E, C ^ - 1)

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A1 + a3 + A5 + A7 = 4, find A2 + A4 + A6