Chapter 2.1, Problem 1PP

Since vectors in ℝⁿ may be regarded as n × 1 matrices, the properties of transposes in Theorem 3 apply to vectors, too. Let

$A=\left[\begin{array}{cc}1& -3\\ -2& 4\end{array}\right]$ and $\text{x}=\left[\begin{array}{c}5\\ 3\end{array}\right]$

Compute (Ax)^T, x^TA^T, xx^T, and x^Tx. Is A^Tx^T defined?