Show that Y1 is that linear combination of the original standardized data that has the most variance.

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Show that Y1 is that linear combination of the original standardized data that has the most variance. That is, show that var(w1Z1 +w2Z2) is maximized (subject to the constraint w21 + w22 = 1) by the weights w1 = 1/√2 = υ11 and w2 = 1/√2 = υ12.
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