A E R"X", Q e R"Xn and Q > 0, C e R™×n. For a given X € R"Xn and X > 0, define the operator h as follows: h(X) AX A' + Q. Assume AA' > I. Prove that Tr (h(X)) > Tr(X) always holds for any X > 0.

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

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Q: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==

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Q: e equation of

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Q: Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) and f(xy) =…

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Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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Q: a. Suppose that ƒ(x) = g(x³) + eg(3x) where g' and g" exist. Find f' and f" in terms of g' and g".…

A: Here we have given a composition of a function as given below.

Q: If z is implicitly defined as a function of x and y via the equation e² = xyz, compute 33 and 3.

A: The given equation is, ez=xyz. To find: ∂z∂x,∂z∂y. To compute ∂z∂x,∂z∂y : Partially differentiate…

Q: ssuming that f(x) is of the form A - B², write an expression for f(x): x) =

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Q: example of two functions t₁ (n) and t₂(n) that satisfy the relations t₁(n) w(n²), t₂(n) = w(n²) and…

A: Given that the two functions t1(n) and t2(n) that satisfy the relations                t1(n)=ω(n2),…