Let $\omega \in \text{Alt}^{2}(\mathbb{R}^3)$ a $2$-Forms on $\mathbb{R}^3$. Show that it exists $\alpha, \beta \in \text{Alt}^{1}(\mathbb{R}^3)$ such that $\omega = \alpha \wedge \beta$.
2026-03-24 23:55:12.1774396512
Every $2$-Forms on $\mathbb{R}^3$ can be written as edge of $1$-Forms
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Hint: show that every vector $w$ in $\mathbb{R}^3$ is the vector product of two other vectors: $w = u\times v$.