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[Solution] Norm of linear combination of orthonormal vectors. Suppose a_1, ..., a_k are orthonormal n -vectors, and x=β_1 a_1+•s+β_k a_k,

Question: Norm of linear combination of orthonormal vectors. Suppose \(a_{1}, \ldots, a_{k}\) are orthonormal \(n\) -vectors, and \(x=\beta_{1} a_{1}+\cdots+\beta_{k} a_{k}\), where \(\beta_{1}, \ldots, \beta_{k}\) are scalars. Express \(\|x\|\) in terms of \(\beta=\left(\beta_{1}, \ldots, \beta_{k}\right)\).

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