Let f(x1, x2, 3) = 3x + 4x + 3x + 2x1x3. x1 X2 (i) Find...

   

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Let f(x1, x2, 3) = 3x² + 4x² + 3x² + 2x1x3. x1 X2 (i) Find an orthogonal transformation X3 f(x1, T2, T3) to the standard form in the new variables (i.e. the quadratic form containing only square terms in y₁, 92, Y3). (ii) Using the results in (i) show that the minimum value for f(x1, T2, T3)/xx X1 X2 0 is equal to 2. with x = X3 ( Yı Y2 that transforms Y3 Let f(x1, x2, 3) = 3x² + 4x² + 3x² + 2x1x3. x1 X2 (i) Find an orthogonal transformation X3 f(x1, T2, T3) to the standard form in the new variables (i.e. the quadratic form containing only square terms in y₁, 92, Y3). (ii) Using the results in (i) show that the minimum value for f(x1, T2, T3)/xx X1 X2 0 is equal to 2. with x = X3 ( Yı Y2 that transforms Y3