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Proof Prove Property 2 of Theorem 5.7: If u, v,and w are vectors in an inner product
Chapter 5, Problem 91(choose chapter or problem)
Proof Prove Property 2 of Theorem 5.7: If \(\mathbf{u}, \mathbf{v}\), and \(\mathbf{w}\) are vectors in an inner product space V, then \(\langle\mathbf{u}+\mathbf{v}, \mathbf{w}\rangle=\langle\mathbf{u}, \mathbf{w}\rangle+\langle\mathbf{v}, \mathbf{w}\rangle\).
Text Transcription:
u
v
w
langle u + v, w rangle = langle u, w rangle + langle v, w rangle
Questions & Answers
QUESTION:
Proof Prove Property 2 of Theorem 5.7: If \(\mathbf{u}, \mathbf{v}\), and \(\mathbf{w}\) are vectors in an inner product space V, then \(\langle\mathbf{u}+\mathbf{v}, \mathbf{w}\rangle=\langle\mathbf{u}, \mathbf{w}\rangle+\langle\mathbf{v}, \mathbf{w}\rangle\).
Text Transcription:
u
v
w
langle u + v, w rangle = langle u, w rangle + langle v, w rangle
ANSWER:Step 1 of 4
Given that and are vectors in the inner product space , we must prove that