Originally Posted by

**sean.1986** Let $\displaystyle B$ be an $\displaystyle m * m$ matrix with inverse $\displaystyle B^-1$, $\displaystyle c$ an $\displaystyle m$-vector and $\displaystyle 0$ the $\displaystyle m$ dimensional null vector. $\displaystyle A$ is given in the following partitioned form...

$\displaystyle A = \left[ \begin{array}{cccc} B & 0 \\ c^T & 1 \end{array} \right]$

Determine $\displaystyle A^{-1}$ symbolically in a partition form.

For which I get the following...

... [SNIP] ...

$\displaystyle A^{-1} = \left[ \begin{array}{cccc} B^{-1} & 0 \\ -c^TB^{-1} & 1 \end{array} \right]$

Is this correct so far? Yes.

The question then asks the dimension of $\displaystyle A$ and the dimensions of the submatrices in $\displaystyle A^{-1}$.

Am I right in thinking the dimension of A is m+1, the dimension of $\displaystyle B^{-1}$ is m and the dimension of $\displaystyle -c^TB^{-1}$ is 1?