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Show that in general there are three val...

Show that in general there are three values of t for which the following system of equations has a non- trival solution `(a-t)x+by+cz=0, bx+(c-t)y+az=0 ` and `cx+ay+(b-t)z=0`.
Express the product of these values of t in the form of a determinant.

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The correct Answer is:
`|{:(a,b,c),(b,c,a),(c,a,b):}|`
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