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**1. Homework Statement**

A = [ b c ... 0000000000000000000 ]

[ c b c ... .000000000000000 0]

[ ... ]

[ 000000000000000000 c b c ]

[ 000000000000000000 b c ]

where a,b are real. This matrix is tridigonal and symmetric.

I need to show that this matrix has e-values lamda_i = b +2cos((i * pi)/(N+1))

and e-vectors x_i = [sin ((i* pi)/(N+1), sin ((2*i*pi)/(N+1)), ...., sin((N*i*pi)/(N+1))]

**2. Homework Equations**

**3. The Attempt at a Solution**

I could find the deterministic equation to find the e-values but i don't see how that gives rise to trigonometric functions.