Least Square Error The 2-norm of the residual ||b - Ax||_2, is a useful metric w

Question

Least Square Error The 2-norm of the residual ||b - Ax||_2, is a useful metric when solving the least squares problem Ax b. Suppose we solve the least squares problem exactly without any loss of precision from rounding error, what can we say about the value of the residual in general? The residual will be minimized, but must be greater than zero. The residual will be minimized, but will not necessarily be equal to zero. The residual will be zero. The residual will be greater than zero, but less than one.

Explanation / Answer

If the Least squares problem can be solved exactly then the residual wiil be zero

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