Question 2 We are going to find the condition necessary for

Question 2: We are going to find the condition necessary for 1 (SCI 1 ari) 2. AS we saw in class, in general 1 ar? (YC 1 ai 2. But under some very specific conditions, 1 i) is true. a) For n 2, write explicitly (without using the symbol n 1) what 1 r2 is. (3 points) b) For n 2, write explicitly (YCH 1 ai) 2. (3 points) c) Then what has to be true of ar 1 and T2 for Li 1 r? i 1 ari) to hold when n 2? 3 points

Solution

a.

Sum( xi^2), n = 1, 2 = x1^2 + x2^2 [ANSWER]

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B.

[Sum (xi), n = 1,2]^2 = (x1 + x2)^2 = x1^2 + 2 x1 x2 + x2^2 [ANSWER]

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C.

For them to be equal, it has to be that

x1^2 + x2^2 = x1^2 + 2 x1 x2 + x2^2

0 = 2 x1 x2

Thus,

x1 x2 = 0

Therefore,

x1 = 0 or x2 = 0 [ANSWER]