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Linear AlgebraMediumOrthogonality & Least Squares

Orthogonality & Least Squares · Medium problem

Three direction readings to a beacon give the overdetermined system x=3x=3, y=4y=4, x+y=8x+y=8 for a position offset (x,y)(x,y) (inconsistent, since 3+4≠83+4\ne8). Find the distance from the origin to the least-squares estimate of (x,y)(x,y).