It is a general rule that for multivariate data $\boldsymbol{X}$ and a matrix $\boldsymbol{A}$, their entropy is
$$h(\boldsymbol{A} \boldsymbol{X}) = h(\boldsymbol{X}) + \ln |\det \boldsymbol{A}|$$ (see https://en.wikipedia.org/wiki/Differential_entropy#Properties_of_differential_entropy).
What is the rule for the entropy of $\boldsymbol{X}$ multiplied by a vector $\boldsymbol{b}$?
$$ h(\boldsymbol{X} \boldsymbol{b} ) = ?$$