To verify: That the mapping defined by 〈 v , w 〉 = k v 1 w 1 + k 2 v 2 w 2 + ⋯ + k n v n w n is a valid inner product on ℝ n if and only if the constants, k 1 , k 2 , … , k n are all positive.

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Chapter 5.1, Problem 28P

To determine

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

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Answer 2

Question

Chapter 5.1, Problem 28P

To determine

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

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Answer 3

Question

Chapter 5.1, Problem 28P

To determine

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

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Answer 4

Question

Chapter 5.1, Problem 28P

To determine

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

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Answer 5

Chapter 5.1, Problem 28P

To determine

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

Answer 6

Chapter 5.1, Problem 28P

To determine

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

Answer 7

Chapter 5.1, Problem 28P

To determine

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

Answer 8

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Answer 9

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Answer 11

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To verify: That the mapping defined by 〈 v , w 〉 = k v 1 w 1 + k 2 v 2 w 2 + ⋯ + k n v n w n is a valid inner product on ℝ n if and only if the constants, k 1 , k 2 , … , k n are all positive.

Solution Summary: The author explains that the mapping defined by langle v,wrangle =kv_1 if the constants are all positive is verified.

Videos

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

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Chapter 5 Solutions

To verify: That the mapping defined by 〈 v , w 〉 = k v 1 w 1 + k 2 v 2 w 2 + ⋯ + k n v n w n is a valid inner product on ℝ n if and only if the constants, k 1 , k 2 , … , k n are all positive.

Solution Summary: The author explains that the mapping defined by langle v,wrangle =kv_1 if the constants are all positive is verified.

Videos

To verify: That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.

Want to see the full answer?

Chapter 5 Solutions

To verify:

That the mapping defined by 〈v,w〉=kv1w1+k2v2w2+⋯+knvnwn is a valid inner product on ℝn if and only if the constants, k1,k2,…,kn are all positive.