1. Let x, y ∈ Rn be two non-zero vectors. The least squares approximation of y in span {x} is the vector cx, with c ∈ R, that minimises the expression ∥y − cx∥^2.
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- Find an expression for the minimiser cˆ in terms of x and y.
- Express the approximation error ∥y − cˆx∥ in terms of y and the angle θ between x and y. As
always, simplify your answer as far as possible.
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