Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F = (x - y)i + (x + y)j; C is the triangle with vertices at (0, 0), (2, 0), and (0,4) O 32 8 0 16

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: Given that t2y'=4y2+ty+16t2 , y(1)=2 for all t≥1 Now y'=4y2+ty+16t2t2y'=4y2t2+yt+16Put…

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A: First write them in the vector for  F = 11i -2 j E = 5i +3j C = 6i - 3j D = -2j

Q: then: -4 1 0 1 0 0 1 -4 1 0 1 0 ⇒ Au = 114000 -4 B. 1 0 0 1 0 0 0 1 -4 1 0 1 -4 1 0 1 -4 ru2,27 U3,2…

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Q: FIND THE VALUE OF MATRIC C iF C=AB A = 2 1 8 2 3 3 6 4 4 ليا 3 B = "G9 4 3 7 S ہ

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A: Range of the matrix is the column space of the matrix.

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A: Since F is not conservative so we can not solve the part b and c.

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A: We will solve both these questions one by one .

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Q: Find bases for the four fundamental spaces of A. [1 2] 36 A=

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A: Sx=S0x=1+b0x-1-d0x-131≤x≤2S1x=1+b1x-2+c1x-22+d1x-232≤x≤3 S interpolates 1,1, 2,1, 3,0

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Q: III. Graphical Representation of Frequency Distribution Observe the bar graph below which is…

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A: Given Data: Let us consider the given data, Propositions and quantifiers Let x, y ∈ {2, 3, 4}. For…