Advanced Math Archive: Questions from July 16, 2022
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b) Given the vector field \[ \mathbf{F}(x, y, z)=3 z \cos x \mathbf{i}+x \ln y \mathbf{j}+e^{z} \tan x \mathbf{k} \] Determine i. \( \operatorname{div} \mathbf{F} \), (2 marks) ii. \( \nabla \times \m1 answer -
a) The eigenvalues of the matrix are 3 and 6. Find the geometric multiplicity of each one, show work. b)the vectors ... are eigen vectors of the matrix. Find vectors v3 and v4 such that [v1,v2,v3,v4]
Eonsfateremamiaurzesimenterial \( A=\left(\begin{array}{cccc}5 & 0 & -1 & 1 \\ 0 & 6 & 0 & 0 \\ -1 & 0 & 5 & 1 \\ 1 & 0 & 1 & 5\end{array}\right) \) Se sabe que los valores propios de \( A \) son \( \1 answer -
Find all the second partial derivatives. \[ \begin{array}{c} f(x, y)=x^{8} y^{5}+3 x^{9} y \\ f_{x x}(x, y)=32 x^{3} 12 y^{2}+216 x^{7} y \\ f_{x y}(x, y)=40 x^{7} y^{4}+27 x^{8} y \\ f_{y x}(x, y)= \1 answer -
Consider linear transformation T Find an expression T(x,y)
Considerela transformación lineal \( T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3} \) determinada por \[ T\left(\begin{array}{l} 5 \\ 2 \end{array}\right)=\left(\begin{array}{c} 1 \\ 3 \\ -2 \end{arra3 answers -
1 answer
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Use the Chain Rule to find \( \partial z / \partial s \) and \( \partial z / \partial t \). \[ z=\arcsin (x-y), \quad x=s^{2}+t^{2}, \quad y=1-8 s t \] \[ \begin{array}{l} \frac{\partial z}{\partial s1 answer -
1 answer
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Given f(x,y)=cos(−6x−5y)f(x,y)=cos(-6x-5y), find
Given \( f(x, y)=\cos (-6 x-5 y) \), find \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y y}(x, y)= \]3 answers -
1 answer