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b show that every inner product space is a normed space and every hilbert space is banach space and the converses of both the statements may not be true give examples 71607

b show that every inner product space is a normed space and every hilbert space is banach space and the converses of both the statements may not be true give examples 71607

VIDEO ANSWER: Hi. So in this question in the first part, we have to give an example when every normed space is not an inner product space. So that means R squa…

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(a) Show that in an inner product space, x ⊥ y if and only if we have ||x ay|| = ||x - ay|| for all scalars α.(b) Show that in an inner product space, x ⊥ y if and only if ||x ay|| ≥ ||x|| for all scalars α.

(a) Show that in an inner product space, x ⊥ y if and only if we have ||x ay|| = ||x - ay|| for all scalars α.(b) Show that in an inner product space, x ⊥ y if and only if ||x ay|| ≥ ||x|| for all scalars α.

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(a) Show that in an inner product space, x ⊥ y if and only if we have ||x ay|| = ||x - ay|| for all scalars α.(b) Show that in an inner product space, x ⊥ y if and only if ||x ay|| ≥ ||x|| for all scalars α.

(a) Show that in an inner product space, x ⊥ y if and only if we have …

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