Cholesky decomposition is carried out on the following square matrix $[A]$.
$$[A]=\left[\begin{array}{cc}
8 & -5 \\
-5 & a_{22}
\end{array}\right]$$
Let $l_{\mathrm{ij}}$ and $a_{\mathrm{ij}}$ be the $(\mathrm{i}, \mathrm{j})^{\text {th }}$ elements of matrices $[L]$ and $[A]$, respectively. If the element $l_{22}$ of the decomposed lower triangular matrix $[L]$ is $1.968,$ what is the value (rounded off to the nearest integer) of the element $a_{22}$?
- $5$
- $7$
- $9$
- $11$