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Solved: Proof Prove Property 3 of Theorem 5.7: If u and

Chapter 5, Problem 92

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QUESTION:

Proof Prove Property 3 of Theorem 5.7: If \(\mathbf{u}\) and \(\mathbf{v}\) are vectors in an inner product space V and c is any real number, then \(\langle\mathbf{u}, c \mathbf{v}\rangle=c\langle\mathbf{u}, \mathbf{v}\rangle\).

Text Transcription:

u

v

langle u, cv rangle = c langle u, v rangle

Questions & Answers

QUESTION:

Proof Prove Property 3 of Theorem 5.7: If \(\mathbf{u}\) and \(\mathbf{v}\) are vectors in an inner product space V and c is any real number, then \(\langle\mathbf{u}, c \mathbf{v}\rangle=c\langle\mathbf{u}, \mathbf{v}\rangle\).

Text Transcription:

u

v

langle u, cv rangle = c langle u, v rangle

ANSWER:

Step 1 of 3

Given that  and  are vectors in the inner product space  and  is a scalar, we must prove that

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