Linear Algebra Quiz
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INNER PRODUCT SPACES & ORTHOGONALITY
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Let S={e1,e2,e3}S = \{\mathbf{e}_1, \mathbf{e}_2, \mathbf{e}_3\} be the standard orthonormal basis for R3\mathbb{R}^3, and let T={f1,f2,f3}T = \{\mathbf{f}_1, \mathbf{f}_2, \mathbf{f}_3\} be another orthonormal basis where f1=13(1,1,1)\mathbf{f}_1 = \frac{1}{\sqrt{3}}(1, 1, 1). If the transition matrix from SS to TT has the property that its second column sums to zero, which of the following could be f2\mathbf{f}_2?
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