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

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

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Q: 2) Let f(x,y,z) =x²y³z* Use the Lagrange multiplier method to find the maxi- mum value of f on the…

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Q: In Exercises 47-50, verify that Wy %3D Wex- 47. w In (2x + 3y) 48. w = e + x In y + y Inx

A: NOTE-  As per our guidelines we have to solve only first question. Given data- w = ln ( 2x + 3y ).…

Q: Find the linearization of ƒ(x, y) = x2 - xy + 1/2 y2 + 3 at the point (3, 2).

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Q: Prove that the system of parabola y2= 4a(x+a) is self orthogonal

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Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

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Q: Please solve this problem

A: Given integral is,

Q: Find the scalar equation for the plane passing through the point P=(4, -5, 3) and containing the…

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Q: please solve this linear algebra problem.

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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: Find the point on the graph of z: (x2 + + 4y") at which vector n = - P =

A: Given,  (a)   z=-x2+4y2,   n=8,-80, 2  (b) f(x, y)=ex2+2y at (0, 0)

Q: Determine the Jacobian matrix of the function f:R³ → R³ given by f(x,y,z) = (3x²y+ yx²,4x²yz², 6xz³…

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Q: 2. Use the transformation u = x – 2y, v = 2x + y to find x – 2y 2.x + y Where R is the rectangular…

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Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: Find the linearization of f(x, y,z) = x + y centered at (8,4, 5).

A: Given:fx,y,z=x+y at 8,4,5Formula:Lx,y,z=fx0,y0,z0+fxx0,y0,z0x-x0+fyx0,y0,z0y-y0+fzx0,y0,z0z-z0

Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: Verify, if u = x + y+ z, v = x° + y° + z³ – 3ryz, w = x²+y² + z? – xy – yz – za are functionally…

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Q: The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has the…

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Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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Q: The linear operator T: R2 --> R2  defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?

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Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. 5 x + y + z + W = -7 5x + 3y - z +…

A: Here we have to use cramer rule for solving the system of linear equations

Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: Find the residues of f(z) = z²-2z (z+1)²(z²+4) at all its poles in the finite plane.

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Q: Let A ∈ M nxn(F). Show that A is diagonalizable if and only if At isdiagonalizable

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

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Q: Find the vertex of the paraboloid z=x2+4y2−xy+6x−5y+1

A: The paraboloid is of two type, one is elliptic and another is hyperbolic ,  By suitable choice of…

Q: Find the Wronskian of y = 2x + 3, y2 = x² + 3x, and y, = 1 -1. Use the result to determine if the…

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

Q: What is the Cartesian Product of Z × X × Y, where X = {3,–1}, Y = {m, l, 0} and Z {w,b}.

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Q: suppose that x,y,z∈R3 are such that x.(y×z)≠0. prove that x,y,z are linearly independent.

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Q: Let, T: R3 → R³;T(x, y, z) = (2x + y, y – z,2y + 4z) Find the rank and nullity of T.

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Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: Let T : R² → R³ be the linear map given by [2r1 + 7x2] 2i + 22 Write does the matrix A associated…

A: The given linear map is T:ℝ2→ℝ3Tx1,x2=2x1+7x2, x1-x2, x1+x2 To find the matrix A associated with T…

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

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Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: Let v = and v3 1 for which values of S, v,, V2 , and v3 are linearly %3D V2= %3D indonondont

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Q: Let T: M2x2(R) → M2×2(R) be defined by T(A) = A 2 1 1 %3D Is T diagonalizable? Show work and…

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Q: Show that (x, y) = 4x1y1-7x2Y2 for vectors x = (x1, x2) and y = (V1 Y2) in R2 defines an inner…

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Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

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

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Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

A: Given that ϕ:R3→R3 is defined as ϕx,y,z=2x,4x-y,2x+3yz. Now, ϕ is invertible if ϕ is one-one and…

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

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