Question: 5. Order of vectors in the Gram-Schmidt algorithm. Suppose \[{{a}_{1}},{{a}_{2}}\] is a list of two linearly independent \(n\) -vectors. When we run the Gram-Schmidt algorithm on this list, we obtain the orthonormal vectors \(q_{1}, q_{2}\)

Now suppose we run the Gram-Schmidt algorithm on the list of vectors \(a{{ & }_{2}},{{a}_{1}}\) (i.e., the same vectors, in reverse order). Do we get the orthonormal vectors \(q_{2}, q_{1}\) (i . e . the orthonormal vectors obtained from the original list, in reverse order)? If you believe this is true, give a very brief explanation why. If you believe it is not true, give a simple counter-example.

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