Find diagonal matriy D is similar with A a A = [3 8-5

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

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Q: Find 3xyd A A over the triangular region D with vertices (0, 0) (2, 0), (0, 4)

A: Given ∫∫3xy dA Over region (0,0)(2,0)(0,4)

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A: In this question, we have to check the matrix A is symmetric or not.

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Q: Show that M=abcd ab,cdeR is the set 1) all ) X) matrics.shou that it is under adlition and scaler…

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Q: Let A Find grad(div( A ) %3D

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Q: 2. Suppose A is an m x n matrir, x ɛ Rª and Ax = b. Then b is in 1) R" | 2) R™ 3) RmfnT 4) R™n

A: Given :  A is an mxn matrix , x∈Rn and Ax=b   To find :  b is in which space of the given spaces.

Q: Prove that on average, permutations of length n have H, cycles, where Hn i=1

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Q: A hransfoomation is definad by Hhe axa matox A=-a b-a atb Ifois an odd imtreger, prove %3D ushere a…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

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Q: Prove that MSE(Ô) :

A: Consider, MSEθ^=Eθ^-θ2 Here, θ is parameter and θ^ is an estimator              =Eθ^-Eθ^+Eθ^-θ2 add…

Q: find the'mters ection d Exe sy,z]= [a,0,31++ 4,-2,178 [+sy,z]=[6,-12,--11]+5 [1,2,4]?

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Q: 2. Solve the given SLE using LU-Factorization X, + x, +x3 = 3 X, - x, +4x; =4 2х, + 3x, — 5х, %3D 0

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Q: 5. Prove that if A and B are similar then dim(ker(A)) = dim(ker(B)).

A: We have to prove dim(ker(A)) = dim(ker(B)).

Q: Con sider Sam ple X,, X2,.., Xg from a NC8,4). Find the Coverage Probabilit a of interval [x-2, +2].

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Q: Q: Prove that tim %3D

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Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

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Q: 3) Find the mZT= %3D

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Q: Prove that on average, permutations of length n have H, cycles, where Σ Hn i=1

A: We will take an arbitrary set containing n elements and observe the required permutations.

Q: If A and B is a symmeyric, proof that AB-BA is a skew symmetric?

A: We know that a symmetric matrix is a square matrix that is equal to its transpose and a…

Q: 2. Solve the given SLE using LU-Factorization X, + x, +xz = 3 x, - x, +4x; = 4 2х, + 3x, — 5х, %3D0…

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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: 1Q/Give an examfle-of a frouf A-BER such thet (AUB)"= > 22/Prove thetRis aferfect cfaee

A: Question from group theory. NOTE- As per our guidelines we are supposed to answer only one question,…

Q: A, Az, An are independert,2) PLiln)=r9)-1), where Bi is eitler Ai or Ai for izlityn in please proof…

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Q: 10. Triangle JLM with verfices J(-5, 7), L(8, 3), and M(-3, -1): (0, - 5)

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Q: 3. 2. If A is 2x2 matri x aud Á = A, but %3D A+ A. show that A= 0

A: The solution is :

Q: In(z,) + In(-v3 – 1) = In(2) +i %3D

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Q: 5. GIVEN 2 AND a) FIN D OF V ONTO THE THE PROJECTION COLUMN SPACE OF A. - N MI

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Q: Find the charecteristic yfalynemicl matrin g the fellewing 3 -2 e 2

A: the given matrix is: 400532-202 we have to find the characteristic polynomial of the given matrix.

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Q: Find ff 3xydA over the triangular region D with vertices (0,0) (2,0), (0, 4)

A: We will solve the problem

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Q: 7. Find a direct way of showing that the (2, 2)-entry of a 3 x 3 magic square with weight w must be…

A: Use the common form of 3×3 square matrix with weight w  to find (2,2) entry

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Q: Bla) 31 compute measurable

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Q: bet T be the relctiom an Axa olfined oy (Xı4) T(Ziwl iff xy=ZLW. Axa oifined oy Dine that T is an…

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