Statement#

Prove that the standard basis vectors in $\mathbb{R}^3$:

$\mathbf{e}_1 = (1, 0, 0), \quad \mathbf{e}_2 = (0, 1, 0), \quad \mathbf{e}_3 = (0, 0, 1)$

are linearly independent.

Required Topics#

• Definition of linear independence
• Systems of linear equations
• Vector spaces

Solution#

Solution coming soon.