V(x1, x2, x3, x4) = (x2 x1)(x3 x1)(x3 x2) x (x4 x1)(x4...

 

 
 

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V(x1, x2, x3, x4) = (x2 − x1)(x3 – x1)(x3 – x2) x (x4 – x1)(x4 – x2)(x4 – x3) Prove this as follows. Given x1, x2, and, x3. define the cubic polynomial P(y) to be P(y) = 1x₁x²x² 1 X2 I 1.2 p3. Because P(x1) = P(x2) = P(x3) = 0 (why?), the roots of P(y) are x1, x2, and x3. It follows that P(y) = k(y-x1)(y-x2)(y-x3) where k is the coefficient of y3 in P(y). Finally, observe that expansion of the 4 x 4 determinant in (26) along its last row gives k= V(x1, x2, x3.)and that V(x1, x2, x3,x4) =P(x4). Problem Show by direct computation that V (a, b) = b − a and that - 1aa² V(a,b,c) = 1 b b² = (b − a)(ca)(c-b). 1 V(x1, x2, x3, x4) = (x2 − x1)(x3 – x1)(x3 – x2) x (x4 – x1)(x4 – x2)(x4 – x3) Prove this as follows. Given x1, x2, and, x3. define the cubic polynomial P(y) to be P(y) = 1x₁x²x² 1 X2 I 1.2 p3. Because P(x1) = P(x2) = P(x3) = 0 (why?), the roots of P(y) are x1, x2, and x3. It follows that P(y) = k(y-x1)(y-x2)(y-x3) where k is the coefficient of y3 in P(y). Finally, observe that expansion of the 4 x 4 determinant in (26) along its last row gives k= V(x1, x2, x3.)and that V(x1, x2, x3,x4) =P(x4). Problem Show by direct computation that V (a, b) = b − a and that - 1aa² V(a,b,c) = 1 b b² = (b − a)(ca)(c-b). 1

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ANSWER Lets follow the steps outlined in your proof and compute Va b and Va b c as described Define ... View the full answer