Suppose I have a random vector $\boldsymbol{Z}$, if I can prove that for $\forall \boldsymbol{\lambda} \neq \boldsymbol{0}$ where $\boldsymbol{\lambda}$ is a fixed vector, not a random vector,

$\boldsymbol{\lambda}^{\text{T}}\boldsymbol{Z} \sim N(0, \boldsymbol{\lambda}^{\text{T}}\boldsymbol{C}\boldsymbol{\lambda})$

where $\boldsymbol{C}$ is a positive definite matrix. Can I establish accordingly, that 

$\boldsymbol{Z} \sim N(\boldsymbol{0}, \boldsymbol{C})$

?