questions 1, step 1, correction of a typo
f n ( a ) = ∑ j = 0 n ( 2 n j ) a 2 n − j ( 1 − a ) j = 1 − ∑ j = n + 1 2 n ( 2 n j ) a 2 n − j ( 1 − a ) j {\displaystyle f_{n}(a)=\sum _{j=0}^{n}{2n \choose j}a^{2n-j}(1-a)^{j}=1-\sum _{j=n+1}^{2n}{2n \choose j}a^{2n-j}(1-a)^{j}~}
questions 3, correction of a typo
( e 1 0 0 0 ) = g ( e 0 0 0 ) g − 1 {\displaystyle {\begin{pmatrix}e_{1}&0\\0&0\end{pmatrix}}=g{\begin{pmatrix}e&0\\0&0\end{pmatrix}}g^{-1}}
