Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice
Define $s(P,Q)=\sum_{i=1}^nP[i]Q[i]$. A set L of nonzero ten-dimensional real vectors satisfies s(P,Q)=0 for every distinct pair. Find the maximum |L|.
Nonzero pairwise orthogonal vectors are linearly independent: taking the inner product of a linear dependence with each vector forces its coefficient to zero. There can be at most ten independent vectors in ten dimensions. The ten coordinate basis vectors attain the bound, so B.
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