Evaluate det(A) by using expansion along a row or col- umn, given 1 2 1 3 4 A = -2 -1 1 1 -1

Q: find the projection of v onto u.

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Q: If A is invertable then A is diagonalizable. Select one: O True O False

A: If a matrix A of order nxn is invertiable then it has n disctinct eigen values.  And corresponding…

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Q: В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

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Q: Compute the orthogonal projection of ữ'onto 7. Use the square root symbol 'V' where needed to give…

A: Projection of u→ onto v→ is , projv→u→=u→.v→v→.v→v→

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

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A: Given: A mapping from R4 to R6 by T(x)=Ax Find how many rows and columns having the matrix A

Q: 5. What is UF, where F = Ø? Prove the correctness of your %3D | computation. answer

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Q: 4) Using tensor formalism, i.e. Kronecker delta, Levi-Civita symbol, and Einstein's summation…

A: Consider the given vector identity, A→×B→×C→=B→A→·C→-C→A→·B→ By using Levi-Civita tensor method,…

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Q: -find the rank of any inner product of tensors A and B?s 25

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Q: Using OLS or any other suitable method, Prove that E(B1) = B1 %3D E(Bo) = Bo %3D

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Q: (a) Determine whether the field F(r, y, 2) = (-2, 2, -2az - 62) is conservative or not.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Let (An) and (Bn) be (Fn)-martingales on (2, F, P) and let Cn = A - Bn. Show that E [(Am - An) |Fn]…

A: Solution:

Q: Let { = fo + ū and 7 = no + ở so that quaternion multiplication gives §n = £ono + £oð + noũ + ữỡ.…

A: are ξ,η are quaternion numbers So, Let  ξ=ξ0+iξ1+ξ0+Iε2+kξ3 u→=iξ1+ξ0+Iε2+kξ3 and η=η0+iη1+Iη2+kη3…

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Q: Which of the centroid(s) are trivial

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Q: Let v=(-2,3,0,6), find all scalars k such that |kv|=5 LUTION

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Q: Find ATA and AA". 2 0 1 %3D -1 4 2 (a) ATA 1 1 (b) AAT 21 Which of the products are symmetric?…

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Q: Find bases for row( A) and col( A) in th e given exercises using AT.

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Q: Find all valus of z such that (5 + z)6 = (1+ i)z6

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Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

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Q: Computed( u, v) relative to the Euclidean norm, the sum norm, and the max norm.

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Q: Soluti 03 16. A 11 22 1 Let Ax- b be a linear svstem of n eauations in n unknowns, and assume that A

A: Given: A = 03-2114225, b = 75-2  and Ax = b To find: The value of matrix x.

Q: Find a mat rix P such that 30 P%= 1 2 30 0 2 1 0 OAP = %3D 3 -1] 1 0 OB P -3 1 -1 0 OcP = %3D 1 0…

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Q: Determine a scalar r such that Ax = rx, where

A: Matrix: A=12-11014-45x=-12141AX=12-11014-45.-12141

Q: Compute the subdifferential of f(x) = max(1-r,0), for r E Rn.

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Q: Find A'A and AA". -1 1 4 A = 2 0 2 (a) ATA (Б) ААТ Which of the products are symmetric? (Select all…

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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: Evaluate the integral 108 - 2y/E+ 4ydzdy, 4 where A is the parallelogram with vertices (0,0), (),…

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Q: Let u = and Compute the area of the parallelogram determined by four 3. II

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Q: Find the resolvent kernel and Solut of ya) = I+5(1-3x+).y(t).d by Alternative procedure

A: Given Integral equation is y(x)=1+∫01(1-3xt)y(t)dt               (1) The general form of integral…

Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: Q2. (e) Verify that the Cauchy-Schwarz inequality holds. įu=(-3,1,0), v=(2,-1,3) uu=(0,2,2,1),…

A: Cauchy-Schwarz inequality relates the inner product of two vectors and their norms.

Q: Let ū = 2i – k and ī = i+3j + k. Compute |ū], |T], ū x ī, and Projzū.

A: Solution is here

Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: z? f(2) = 1-z* 4

A: We use the fact that the 1/(1-z)= 1+z+z2+z3+z4+......

Q: linear operator L: BC[0, 1] → BC[0, 1] defined by Си — и" — 2и 1 the sup norm.

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Q: Find all the joint moments m,1, n and k= 0, 1. . .

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Q: 1. Let R? have the inner product of Example 1, and let x = (1, 1) and y = (5, – 1). a. Find ||x||,…

A: Let R2 have inner product s.t.if u= u1,u2 and v=v1,v2 betwo vectors in R2then <u,v>=u.v…

Q: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A).

A: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A). For any scalar k, we need to…

Q: find Fourier sertes [o, 2w] an くxく下 O f cx)= (2 2下-X πく*く 2x fcx) = こ 2.

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Find leng th of the Cardioid Vsa6 from e -oto0 - 1 %3D

A: Use the formula of the length of the polar curve. L=∫0πr2+drdθ2dθ Here, r=aθ3 and drdθ=ddθ(aθ3)=3aθ2…

Q: (a) Verify the Cayley-Hamilton theorem. (b)  Use the theorem to express A2 and A3 as linear…

A: Part (a), Let, A=4-112 Now, the characteristic equation of A,…

Q: Let A and P be an n x n matricies, where P is invertible. Show that det(PA(P-1))=detA.

A: To show that,

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…