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I tried this problem but I failed. It is a symmetric matrix, it should be orthogonal diagonalizable. If I can find the eigenvalues and eigenvectors of this matrix, then i can calculate it easily. The answer should be the product of their eigenvalues.

However I am unable to find the eigenvalues since it is a nxn matrix. (I used online calculator to checke, the eigenvalues should be $(n-1)$ times $(x-a)$ and $1 \times [x-(n-1)a]$ May anyone give me any tips on this problem?

TShiong
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Dec 15 '22 at 18:55
  • Finding eigenvalues/eigenvectors is far harder than finding the determinant. Usually you want to do some sort of inductive/recursive argument with matrices like this. – Ted Shifrin Dec 15 '22 at 19:00
  • Please don't use pictures. See here, why. Use MathJax. Here is a tutorial. – Dietrich Burde Dec 15 '22 at 19:15

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