tions in Problems 1–11. Describe the kernel. 1. T:R? → R², T(x, y) = (-x, y) 2. T:R' → R?, T(x, у, г) %3D (2x + 3y – z, -x + 4y + 6z) 3. T:R' - R', T(x, y, z) = (x, y, 0) 4. T:R → R', T(x, у. г) %3 (х — г.х — 2у. у — г) 5. D:C' - с, D(f) = f' 6. D? : C? → C, D²(f) = f" 7. L : C' → C, Li(y) = y' + p(t)y L„(y) = y(n) +a,(1) yln-1) + ..+ an-1(t)y' + a,(1)y 8. L, : C" → C, 9. T :М23 — М32. Т(А) 3D АT a 0 01 0 e 0 0 0 a 10. Т: Мзз - M33. T d e f = 11. Т : Р, — Р, T(p) = p(t) dt for fixed x

Q: T(1,1)=(5,0) Let T:²²be defined as, T(1,0)=(2,6) Then, T(3,2)=(12,6) (a) T(0,1)=(-3,6) (b)…

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Q: • If the lines of regression of Y on X and X on Y are respectively = 0 and a,x + b¡y + c, azx + b2y…

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Q: 6. Evaluate − (x²+y²+z²) √x² + y²+z² where E is the region bounded between the spheres x² + y² + z²…

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Q: 8. Evaluate •S.F.d F-dr where F(x, y, z) = (-7 sin(7x)-yz, π cos(ny)-xz, -xy) and C is any path that…

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Q: If F(x, y, z) = (x²z, –2xz, yz), then curl F(6, –3, 1) equals %3D O (12, 39, –5) O (9,34, 2) O (13,…

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Q: {X, p, {a}, {b, c}}, Y = {1,2,3}, t* = {Y, ¢,{1},{1, 2}} and a function (b) Let X = {a,b, c}, t =…

A: We will use definition of open map and closed map.

Q: 29. Calculate /| (xy +e*)ds, where S is the triangle in Figure 18 with vertices (0,0, 3), (1,0, 2),…

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Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: 5. If Z1 = V3 – 2i, Z2 = -i+1 and Z3 = 4i – 2. Evaluate (i) Re{3Z} – 5Z7 + 2Z}} (ii) |(1+ Z2+ Z3)(i…

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Q: Determines the distance between the left right.

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Q: 4. Problem 4 For what values of r are the vectors {(1). (+²)} linearly independent?

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Q: Evaluate fry²dx + x^dy, where C' is the rectangle with vertices (0,0), (4,0), (4,1), and (0,1).

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Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: r3 + y = Ty, then y = 32 3» ყ passos " 1 — 34 + ყ 3.72 O x - 3x² + y 3y² O 32 — y — 3g2 - lf

A: Given

Q: critical point of y : +3 х — 2 O 1,-1 O 3/2,-27/4 O 0,0 О 3, 27

A: Solution:Giveny=x3x-2Formula:uv'=vu'-uv'v2

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as

Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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Q: 10.37. Let A ={1,2,3,4}, B={a,b,c} and C = {w, x, y, z} . Consider the functions f : A → B and g: B…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: center (x, y) = radius r= -10 -10 10 5 -10 y 10r 5 -10 5 10 10 O -10 -10 -5 -5 -10 -10 10 5 y 10 5 X…

A: Given equation of a circle.

Q: 9. If t(x,y)(a) is a translation defined by t(x,y)(a,0) = (x+a₂y+ß), determine t(5,8) (2-2)* a.…

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Q: 3. (Section 17.6) Determine the upward flux of F = through the part of z = x2 + y2 below z = 2.

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Q: 13. [P] Particle 1 starts at point (3, 1, 1) and particle 2 starts at point (10, 5, -4); at t = 0,…

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Q: function

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