Let matrix $X = \begin{bmatrix}x_1 & x_2 \end{bmatrix}, \; \Sigma = \begin{bmatrix}a_{1,1} & a_{1,2}
a_{2,1} & a_{2,2}\end{bmatrix}$. Assume none of the elements are zero in $X,\Sigma$. Let $X^T$ denote the transpose of vector $X.$ Select all that are true about $X\Sigma X^T$
- It is equal to $\begin{bmatrix}x_1^2a_{1,1} & x_1x_2a_{1,2}\\
x_1x_2a_{2,1} & x^2_2a_{2,2} \end{bmatrix}$.
- Is it equal to $X^T \Sigma X$.
- It is non-singular.
- None of the above are true.
