Chapter 2.1, Problem 27E

In Exercises 27 and 28, view vectors in ℝⁿ as n × 1 matrices. For u and v in ℝⁿ the matrix product u^Tv is a 1 × 1 matrix, called the scalar product, or inner product, of u and v. It is usually written as a single real number without brackets. The matrix product uv^T is an n × n matrix, called the outer product of u and v. The I products u^Tv and uv^T will appear later in die text.

27. Let u = $\left[\begin{array}{l}-2\\ 3\\ -4\end{array}\right]$ and v = $\left[\begin{array}{l}a\\ b\\ c\end{array}\right]$.

Compute u^T v. v^T u, uv^T, and vu^T.