For the functions w =xy + yz + xz, x = 3u + v, y= 3u - v, and z = uv, express , and , using the chain rule and by expressing w directly in terms of u and v before dw dw and differentiating. Then evaluate at the point (u,v) = du dv dw dw and du Express as functions of u and v. dv dw du

Q: 2xy// + (x + 1)y/ +3y = 0

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Q: Decide if the following functions are linearly independent in the interval (-00, 00) f1(2) = 1+r,…

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Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

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Q: For the function h(x,y) = 6x + 7y xy-5 7 əh find and ?x əh dy

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Q: Find functions f and g so that fo g=H. H(x) =x +4 Choose the correct pair of functions. OA. OB. f(x)…

A: Solution

Q: Find f.(x, y) and f,(x, y) for f(x, y) 3x3 + 8y? – 6x + 4y and evaluate each at f(4, 5). f.(x, y) =…

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Q: Given u = (-2, 4) and = (1, 6), find 3(uw).

A: The vectors are given by u→ = -2, 4w→ = 1, 6 To evaluate: The value of 3u→·w→

Q: Find Vf(a), given the following data. 91 Calculate 91, 92 and 93 such that Vf(a) = 92 93. 91 92 93 =…

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Q: Let u and v be the linear functions defined asu(x)=2x+3,v(u)=3x-2.Find the compositions u*v and v*u.…

A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: f(x, y) = x² + y² + 64xy

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Q: Differentiate the function. u' +71

A: Topic = Derivative

Q: Find all functions from X = {a,b} to Y = {p,r,t}.

A: Given :- To find all functions from X = a,b to Y= p,r,t.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.