Find a change of variables that reduces the quadratic form to a sum or differenc

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Find a change of variables that reduces the quadratic form to a sum or difference of squares, and express the quadratic form in terms of the new variables. 10x21 + 10x22 - 10x1x2 A substitution x = Py that eliminates cross-product terms is x1 = y1 - y2, x2 = y2. The new Quadratic form is 5y21 + 15y22. A substitution x = Py that eliminates cross-product terms is x1 = 1/2y1 - 1/2y2, x2 = 1/2y1 + 1/2y2, The new quadratic form is 10y21 + 75 y22. A substitution x = Py that eliminates cross-product terms is x1 = y1 - 10y2, x2 = y1 + 10y2. The new quadratic form is 10y21 + 75y22. A substitution x = Py that eliminates cross-product terms is x1 = 1/2y1 - 1/2y2, x2 = 1/2y1 + 1/2y2. The new quadratic form is 5y21 + 15y22. A substitution x = Py that eliminates cross-product terms is X1 =1/2y1 - 1/2y2, X2 =1/2y1 + 1/2y2,. The new quadratic form is 10Y21 - 20y22 .

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