James Chen

I'm taking my first abstract algebra course and I understand the formal definition of a group: - Closure: $\forall a, b \in G, a \cdot b \in G$ - Associativity: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$ - Identity: $\exists e \in G$ such that $e \cdot a = a \cdot e = a$ - Inverse: $\forall a \in G, \exists a^{-1} \in G$ such that $a \cdot a^{-1} = a^{-1} \cdot a = e$

I can handle $2 \times 2$ matrices, but finding eigenvalues of a $3 \times 3$ matrix is more challenging. For example: $$A = \begin{pmatrix} 2 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 1 & 2 \end{pmatrix}$$

I need to understand the simplex algorithm for solving linear programming problems.

Consider the problem: