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Solved: Proof Prove Property 3 of Theorem 5.7: If u and
Chapter 5, Problem 92(choose chapter or problem)
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