4) Find the adjoint of the operator Lu = u" + 4u'- 3u, where u'(0) = -4u(0), u(1) = -4u(1).

Q: Compute Div(F) and Curl(F): F--(4y-1) i+yj+(-3y) k

A:

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 ,…

A:

Q: Rit +1 ,2it ait -| = î7 e +iz (1-iz)eit 1+iz %3D iz

A:

Q: ). Show that V - u -ly- tan' u < V - u 1- if 0<u<v, < tan 1+v? 1+u 4 2< tan 4 25 3 and deduce that 3…

A:

Q: what happened to the 1(1-lambda) part in the first line

A: Given

Q: 4メーY - 3z = -8 -x+3y - 2z =5 2x + 2y -5z =7 ニ

A:

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

A:

Q: { (0,3), (0,1) is linearly independent in R? ylgn O Ins

A: The given vectors are  (0, 3) and (0, 1) To find whether they are linearly dependent or not

Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the…

A:

Q: Use the Wronskian and any needed theorems to show that f1 = sin x + 2x2 and f2 = e3x are linearly…

A:

Q: Write down the general solution of Ax = b in parametric vector form.

A:

Q: 2x+ 3y-z =1 4x + y-3z = 11 3x-2y +5z = 21 | %3D

A: Solution:

Q: as the sum of two orthogonal orthogonal to ư

A:

Q: Use chain rule to find az at (u, v) = (1, 1) if

A:

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

A:

Q: Let UsX +Sinx Deter of X 0n [0,)where ļ Find . derivalire fa 2x+1 x²+7 te tn 6x+

A:

Q: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

A:

Q: Which elements are invertible in Z4[x,y]?

A: W need to find elements which are invertible inZ4x,y.

Q: prove that the covariant derivate satisfies leibniz's rule

A: The main reason behind the covariant derivative satisfying Leibniz's rule is it maintains chain rule…

Q: #2. Find invertible matrxes B and C SO C M.B =

A:

Q: I want to convert z=x2−2xy+1 to tensor product blossom and compute the control points if its over…

A:

Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

A:

Q: Find y,(x) if y = In(In(Inx)).

A:

Q: Compute Jx²z ds where C is the line segment from (0,6,–1) to (4,1,5).

A: The objective is to compute ∫Cx2zds where C is line segment from  0,6,-1 to 4,1,5

Q: let z- 57 dy .. dy By chain Ruie

A: The objective is to find the second derivative using chain rule.

Q: Find the orthogonal trajection of the family of y=ax

A: In mathematics an orthogonal trajectory is a curve, which intersects any curve of a given pencil of…

Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

A:

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Let æ² + y² + z² = 3xyz, th = 3ryz, th

A: Given that, x2 + y2 + z2 = 3xyz We have to find (del z)/(del x).

Q: 1- -Н(y)-Н(yх) Prove that 2- H(x,y) = H(y) + H(x\y) 3- H(x,y) = H(x) + H(y}x) 4- Н(х., у) %3DН(х) +…

A:

Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: s the linear operator T : R3 --> R3 defined by T (x, y, z) = (2x - 3y + 7z, 5y + z, -z)…

A:

Q: Find the flux of ỹ across S.

A: In this question we need to find the flux across the surface is part of sphere of radius 9.

Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

A:

Q: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

A:

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: Consider the linearizable functions as follows. Find new transformed variables (rª, yª, Bor B as you…

A:

Q: on vectors for t2 0.

A:

Q: 2. Sketch 0 in standard position if cose = 8. and deter %3D

A: Given that: cosθ=-817

Q: Verify the chain rule for jacobian, if y2 u = x + , v = * y2 %3D

A:

Q: 4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are…

A: 4.

Q: 4. Show that u and v are orthogonal if and only if ||u + v||2 = ||u||2 + ||v||2. (Please avoid an…

A: