[Step-by-Step] a. Show that the following vectors form a basis for R^3.


Question: a. Show that the following vectors form a basis for \(\mathbb{R}^{3}\).

\[\left[\begin{array}{l} 1 \\ 1 \\ 0 \end{array}\right],\left[\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right], \text { and }\left[\begin{array}{l} 0 \\ 1 \\ 1 \end{array}\right]\]

b. How can you express an arbitrary vector in \(\mathbb{R}^{3}\) as a linear combination of the above basis vectors?

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