Let ⟨ − , − ⟩ {\displaystyle {}\left\langle -,-\right\rangle } denote a bilinear form on R 2 {\displaystyle {}\mathbb {R} ^{2}} , with the values ⟨ e 1 , e 1 ⟩ = 5 {\displaystyle {}\left\langle e_{1},e_{1}\right\rangle =5} , ⟨ e 1 , e 2 ⟩ = − 4 {\displaystyle {}\left\langle e_{1},e_{2}\right\rangle =-4} , ⟨ e 2 , e 1 ⟩ = 7 {\displaystyle {}\left\langle e_{2},e_{1}\right\rangle =7} , and ⟨ e 2 , e 2 ⟩ = − 3 {\displaystyle {}\left\langle e_{2},e_{2}\right\rangle =-3} . Compute ⟨ ( 3 − 4 ) , ( − 5 − 6 ) ⟩ {\displaystyle {}\left\langle {\begin{pmatrix}3\\-4\end{pmatrix}},{\begin{pmatrix}-5\\-6\end{pmatrix}}\right\rangle } . Is it an inner product?
denote a
bilinear form
on 
, with the values
,
,
,
and
.
Compute 
. Is it an
inner product?
