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(a) Show that in an inner product space, x is orthogonal to y if and only if we have ||x ay||^2 = ||x - ay||^2 for all scalars.(b) Show that in an inner product space, x is orthogonal to y if and only if ||x ay|| = ||x|| for all scalars.

(a) Show that in an inner product space, x is orthogonal to y if and only if we have ||x ay||^2 = ||x - ay||^2 for all scalars.(b) Show that in an inner product space, x is orthogonal to y if

VIDEO ANSWER: We want to prove the relationships that have to do with the inner product. x and y are both non -zero. If the magnitude of x plus alpha y is equa…

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