Solution to Ex. 4.3 is wrong

[FineArtz]

It is clear that

is wrong because $\hat{\mathsf{B}}$ is not a square matrix thus cannot be inversed. The proper way is to expand $\hat{\Sigma}$ and prove $$B(B^T\Sigma B)^{-1}B^T\mu_k = \Sigma^{-1}\mu_k$$.

[YuhangZhou88]

thanks! you are correct

[leonardojoau]

Is it clear to anyone how to prove that last equality given that cannot invert matrix B?