Given a block diagonal matrix $A$ like so:
$A= \begin{bmatrix} B & & \\ & C & \\ & & D \\ \end{bmatrix} $
Given $B$ is symmetric and has real, positive eigenvalues (obviously $B$ is positive-definite), $C$ is
$C = \begin{bmatrix} 11 & -4 \\ 0 & 2 \end{bmatrix} $
and $D$ is
$D = \begin{bmatrix} 11 & -3 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & 3 \\ \end{bmatrix} $
I'm asked to determine whether $C$, $D$ and $A$ are positive-definite. Well, $C$ and $D$ are asymmetric, so obviously we need to stretch the rules and use the definition of positive-definiteness that includes asymmetric matrices, which states that an asymmetric matrix is positive-definite iff its symmetric part (the sum of the matrix plus its transpose, divided by $2$ (optionally)) is positive-definite.
So, calculate the symmetric parts of $C$ and $D$, see if they're positive-definite, easy enough. However, not knowing the data of $B$ (besides its properties) doesn't allow me to calculate the symmetric part of $A$, so I need to work by properties only. What am I not seeing here?