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[See Steps] Gram-Schmidt algorithm. Consider the list of n -vectors

Question: Gram-Schmidt algorithm. Consider the list of \(n\) -vectors

\[a_{1}=\left[\begin{array}{c} 1 \\ 0 \\ 0 \\ \vdots \\ 0 \end{array}\right], \quad a_{2}=\left[\begin{array}{c} 1 \\ 1 \\ 0 \\ \vdots \\ 0 \end{array}\right], \quad \ldots, \quad a_{n}=\left[\begin{array}{c} 1 \\ 1 \\ 1 \\ \vdots \\ 1 \end{array}\right]\]

(The vector \(a_{i}\) has its first \(i\) entries equal to one, and the remaining entries zero.) Describe what happens when you run the Gram-Schmidt algorithm on this list of vectors, i.e., say what \(q_{1}, \ldots, q_{n}\) are. Is \(a_{1}, \ldots, a_{n}\) a basis?

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