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Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the...
(6) Let Q(x) = 2x; -4.01.22-23. Make a change of variable that transforms the quadratic form Q(2) into a quadratic form with no cross-product term.
Consider the quadratic form Q(1, 2, r)2r2r34rs. Write Q(, 2, 3) in the fornm Q(1, 2, z3)xAx for some matrix A to be found, where x-2 T3 Classify Q(x1, r2, r3) as positive definite, negative definite, positive semidefinite, negative semidefinite, or indefinite
Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form Q, and express Q in terms of the new variables. 7x{ + 6x2 + 5x3 - 4X1X2 + 4x2X3 A substitution x = Py that eliminates cross-product terms is X1 = o A substitution x = Py that eliminates cross-product terms is Xi = – -}y.+3y2– žys, x2 = - - Žy2+3y2 +3v3, x3 = - {yı+ {y2– žv3. The new quadratic form is...
4. (15') (a) Find the orthogonal change-of-variable y -5x +42122 – 2x2 has no cross-terms in terms of y. Qī so that the quadratic form QT) = (b) Determine the geometric type of the curve c = Q(7) and sketch a graph as accurately as you can. (c) Determine if Q is positive or negative definite or indefinite or semi-positive/negative definite.
4. (15') (a) Find the orthogonal change-of-variable y -501 + 42102-2-3 has no cross-terms in terms of y. Q7 so that the quadratic form Q(2) (b) Determine the geometric type of the curve c = can. Q() and sketch a graph as accurately as you (c) Determine if Q is positive or negative definite or indefinite or semi-positive/negative definite.
Consider the quadratic form Q(x) xỈ + x2 + x + 4X1X2 + 4x2x3 + 4x3x1. (a) Find the real symmetric matrix A so that Q(X) = XTAX. (b) Find an orthogonal matrix Q so that the change of variables x = Qy transforms the quadratic for Q(x) into one with no cross-product terms, that is, diagonalize the quadratic form (x). Give the transformed quadratic form. (c) Find a vector x of length 1 at which Q(x) is maximized. (d)...
# 1: Consider the following curves in R la) 1822-32 x y + 37 U2 100. l ) 2x2 + 6 x y + 2 y-100. 1c) x2 + 4 x y + 4 y2-10:0. Write them in normal form. Give the change of variables that does this. For example, in 1a) the orthonormal basis of eigenvectors are λί 5,V1 (2,1)'/V5 and λ2 = St ( 100. ) . That is, 45, ½ = (1,-2)t/V5.S ( 1/V 5-2/v/5 ) (V6,...
A polynomial p(x) is an expression in variable x which is in the form axn + bxn-1 + …. + jx + k, where a, b, …, j, k are real numbers, and n is a non-negative integer. n is called the degree of polynomial. Every term in a polynomial consists of a coefficient and an exponent. For example, for the first term axn, a is the coefficient and n is the exponent. This assignment is about representing and computing...
Fatty Acid Metabolism. The reactions of the fatty acid spiral are shown below. Use the description on the left side of the page to classify the reactions and fill in the boxes on the right side of the page Activation Step. The activation of the fatty acid begins by the addition of CoA which will carry the fatty acid from the cytosol into the mitochondria. The product, which is a fatty acid with a CoA attached, is known as a...
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11.8 Multiple committees The eventual goal of this assignment is to compute the total number of ways of forming a collection of committees from an academic department of n professors. The first task is to write a function called committee to compute the number of ways of forming a single committee with members from a collection of n people. This is the same as compușing the number of ways of choosing r people out of n to sit at...