Solution Found!
Let A be a symmetric matrix. Without using the Spectral Theorem, show that if _= , x
Chapter 6, Problem 6(choose chapter or problem)
QUESTION:
Let A be a symmetric matrix. Without using the Spectral Theorem, show that if \(\lambda\ \neq\ \mu\), \(\mathbf{x} \in \mathbf{E}(\lambda), \text { and } \mathbf{y} \in \mathbf{E}(\mu), \text { then } \mathbf{x} \cdot \mathbf{y}=0\).
Questions & Answers
QUESTION:
Let A be a symmetric matrix. Without using the Spectral Theorem, show that if \(\lambda\ \neq\ \mu\), \(\mathbf{x} \in \mathbf{E}(\lambda), \text { and } \mathbf{y} \in \mathbf{E}(\mu), \text { then } \mathbf{x} \cdot \mathbf{y}=0\).
ANSWER:Step 1 of 2
Suppose A is a symmetric matrix and 
To prove that 
Since
