Find the Ker(T) and Rng(T) and their dimensions. T:R → R defined by T(x)= Ax , where 1 -1 A = -3 3 -6 |I

Q: In AMNP, T is the centroid. If MR=30 find MT. N R T M S

A: We are given that T is the centroid and MR=30. We know that the centroid divides each median in a…

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Q: For the given functions, (a) express dt as a function of t, both by using the chain rule and by…

A: Topic = Derivative

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Q: In Exercises 23–30, find Tn centered at x = a for all n. 26. f (x) = e", a =-2

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Q: The linearization at a = 0 to V6+ 5x is A+ Bx. Compute A and B %3D A = %3D B = %3D

A: Consider the given: Let fx=6+5x    at x=af0=6+50f0=6+0f0=6

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Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

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Q: If z = f (u) + g(v), where u = = and v = x ·y. Prove that Q1: x· Zx – y· Zy = y² · Zyy – x² · Zxx…

A: We have z=fu+gv, and u=xy  and v=x.y We need to use the chain rule and prove x.zx-y.zy=y2.zyy-x2.zxx…

Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy +8 at Po(5,5). Then find an upper…

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Q: 4. Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: Let T : (0 → l defined by T(Xn)) = ( n. (a) Prove that TE B(l, l∞) and ||T|| = 1.

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Q: Let f(x, y) xy, x = 1- Vt, and y = 1+ Vt. Find df using the chain rule. dt

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Q: Let / = L, e*dx. The approximation of I using the two-point Gaussian quadrature formula 3.488225…

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Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

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Q: Let T: R2→R2 such that T(1, 0) = (1, 0) and T(0, 1) = (0, 0). (a) Determine T(x, y) for (x, y) in…

A: Given Data T(1,0)=(1,0). T(0,1)=(0,1).   (a) Let, The general expression for the linear…

Q: Consider h(x,y, z) = cos (xy) + eY² + In (xz) at the point P ( 1,0, = 1 Deter-

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Q: 2. In A ABC, X is the centroid. A A If CW = 15, find cx and XW. W, B. If BX = 8, find BY and XY.

A: we know that  centroid is located 23 of the distance from the vertex along the segment that connects…

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Q: dw Use an appropriate form of the chain rule to find dt In(14.x² – 4y + 523); x = ti, y= tổ, z = t-2…

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Q: Q2// A :-Compute for the following at t=1 z= ze", z =t, y=t1

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Q: Consider the solid lih S,: X=4-y² そ=2

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Q: Define T:R → R' by T(x, y, z) = (x-5y+4z, y- 6z). a) Is T one-to-one? Justify your answer. b) Is T…

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Q: Consider the following semilinear first-order PDE ди ди + Y = xe¯u ду (i) Find the general solution…

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Q: 2. Use the Chain Rule to find for z = e¤/y where x = st and y = s2 +t

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Q: Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: Determine DFT X[ej"] of the signal (answer a or b) a) x[n]coswon. b) x(n) = a"u(-n- 1) %3D

A: As it's mentioned in the question to answer between a) or b), so showing steps for only one part. b)…

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension.

Q: For u(x, y, t) aefined on the domain of - o<x<o, - 0 <y<o, and t2 0, solve the PDE du = (1+t)u ду ди…

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Q: Use the Chain Rule to find az/as and əz/ət. Z = tan(u/v), u = 7s + 5t, V = 5s – 7t az ds az at

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Q: Consider ф: C" — C defined by ф(x) %3D х*. a) Kerф %3D (1,-1} b) Kerø = {i,-i} %3D с) Kerф %3D (1,1}…

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Q: Consider the following. w - xy + xz + yz?, x= t, y- 7t, z-7 (a) Find dw/dt using the appropriate…

A: We have to use chain rule to solve the question.

Q: Suppose the goind densiy Runction Xanef y i ginen by frxy) = 44 (ス-8) ○ZXC0,○ ス %3D otheraise…

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Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT>XT. Y T

A: Given a diagram: ZY=ZX To  prove YT&gt;XT

Q: .The primal form of SVR with soft margin is M 1 min |w+CE(6i + &;) i=1 s.t. y) – w"x1) – b < e+ §i,…

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Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

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Q: 41. Let f(x, y, z) =x?y+ y²z. Use the Chain Rule to calculate af/as and af/at (in terms of s and f),…

A: Since f is function of x, y and z.  For partial derivative f with respect to s and t we using chain…

Q: Build the implicit scheme and the simplest iterative process for quasilinear equation ди Ət = * [ ].…

A: Given that: ∂u∂t=∂∂xku∂u∂x, ku=u0.6,0&lt;x&lt;x0t, 0&lt;t⩽2,ux,0=cosπx4, u0,t=ux0t,t=0. The…

Q: Define T: P2 → R by T(p) = S, p(x)dx. Find the kernel of T.

A: According to the given information it is required to find the kernel of linear transformation:

Q: Given F(x, y, z) = (tan y + cosh x Joi 2xy)i + (x sec² y - x² + 1)ĵ - 2zk, evaluate F. dR where C'…

A: Given that,  F→x,y,z=tany+coshx-2xyi^+xsec2y-x2+1j^-2zk^, Therefore, set fx=tany+coshx-2xy…

Q: Let c(t) Use the chain rule to compute (foc)'(t). (cos(t), sin(t), t²) and f(x, y, z) = x² + y² +…

A: The objective is to find the derivative.

Q: Use the chain rule to find ∂w/∂t given w =√ x^2 + y^2 + z^2 and x = cos(st), y = −2s ln(t) and z = s…

A: Solution:Given      w=x2+y2+z2x = cos(st), y = −2s ln(t) and z = s − 3t.To find…