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Homework 3 collaboration area

Question from student regarding HW #3: HW 3 Question: Do to scheduled work travel next week I am trying to get ahead on HW #3. I keep getting stuck on the Eigenvalues. When the directions state to find the spectrum, is it asking for the spectrum of the original matrix or the spectrum of the symmetric, skew-symmetric, orthoganal, hermitian, skew-hermitian, or unitary matrix? I have worked the problems trying to get the spectrum of the original matrix and I am not having much succcess. Thank you.

HWK #3,4,7 on page 329 question: We would want to use variables in these matrices correct? Other wise certain components would indicate a vector space and some would not. Am I correct in stating this?

Question from student regarding HW#3: How much detail is sufficient on page 339, problem 30? Any help with this problem is appreciated.

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I am stuck on where to start with HW3, lesson 7, #30, the proof that the inverse of a square matrix exists iff no eigenvalues are zero.

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