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If x = (x1, x2)T, y = (y1, y2)T and z = (z1, z2)T are arbitrary vectors in R2, prove that

(a) xTx > 0

(b) xTy = yTx

(c) xT(y + z) = xTy + xTz

(a) xTx > 0

(b) xTy = yTx

(c) xT(y + z) = xTy + xTz

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