6. The absolute norm for tensor of two eigenvectors of A=(¯¹) is 3 (b) √3 (d) None of the above (a) 0 (c) √2 O a O b с O d

Q: 15. (i) Let A, B be 2 x 2 matrices over R and vectors x, y in R2 such that Ax = y, By = x, x"y = 0…

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Q: 5. From the eigenvectors of S = AAT/(n-1), find the line and the plane closest to the following…

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Q: Let Q(x) = - 6x, + 2x5 + 8x1X2 - 8x2X3. Find a unit vector x in R' at which Q(x) is maximized,…

A: Given quadratic transform is, Qx=-6x12+2x22+8x1x2-8x2x3.

Q: If X and X are the eigenvectors corresponding to distinct eigenvalues and respectively. then X₁, X,…

A: Explanation of the answer is as follows

Q: 7. Consider the real symmetric 3 x 3 matrices 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 A = B = 1 (i) Find…

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Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

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Q: D: P2> P2 (Dthe differential operator so that D(ax²+bx+c) = 2ax +b); a the standard basis for P2; B…

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Q: 7. The absolute norm for tensor of two eigenvectors of A = (33) is (a) 3 (b) √3 O O b O O d a C (d)…

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Q: 5. The cigenvectors of the matrix [5 4 21 A =4 5 2 2 22] form an eigenspace of A. (a) True (b) Palse…

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Q: 24. Consider the quadratic form Q(x) = -x² - 2y² - z² + 2xy - 2yz a) Find a symmetric matrix A such…

A: As you asked more than 3 sub parts , so I solve first three sub part , please  repost the remaining…

Q: [4 6. Let A = 2 L2 -1 1 -1 61 -21 6. Is 2 an eigenvector? Explain! 81 1

A: We first find the eigenvalue and then find the eigenvectors for the given matrix

Q: 4) Which of the following functions are eigen functions of the operator dx ? Show your proof. a) eax…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Orthonormalize [1, t, t²} in P₂(R) with (p, q) = p(0)q(0) + p(1)q(1) +p(2)q(2) }

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Q: For each Linear Operator: S (x, y) = (2x + y, x + 2y) T(x,y,z) = (z,y,x) to determine: (a) The…

A: Note: Since we can solve at most three subparts in a question, we have solved the first three…

Q: 9. (a). Suppose A is an (nxn)-matrix over the complex numbers satisfying A² = I. Show that A is…

A: What is Minimal Polynomial: A minimal polynomial is related to as square matrix. It is the…

Q: Q#5: [1 Г36 77 a) By using definition, show that the vector x=-2 is an eigenvector of A = 3 3 7 [5 6…

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Q: Let T: R5 → R5  be a linear operator whose characteristic polynomial is pT(x) = (x−3)3(x−5)2. Let V3…

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Q: [7/2-1/2 07 21. Let A = -1/2 7/2 0 Which of the following vectors are eigenvectors of A? Q 0 (a)…

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Q: 3. Find the eigenvalues and cigenspaces, as well as a basis for each eigenspace. (a) [88] 12 3 4 000…

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Q: Q1/ Prove or disprove: A) If A is invertible and k is a nonzero scalar, then kA is invertible and…

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Q: dx which statement about the system at = Ax is true? The characteristic polynomial of A is p(x) = λ²…

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Q: 5 6 0 Compute the quadratic form x'Ax for A = 6 3 1 and each of the following vectors. 0 14 X1 1/ 3…

A: Transpose of each column vector is a row vector. We do simple matrix multiplication to compute the…

Q: Let f(x) = (x – b) Ax + c, where A is symmetric and positive definite matrix, b is a vector and c is…

A: Given that  f(X)=X-bTAX+c, where A is symmetric and positive definite matrix, b is a vector and cis…

Q: Let p(λ) be the characteristic polynomial of the 4 × 4 ma- trix A. Using algebra, you compute the…

A: Given that A is a matrix of order 4×4 and λ be the eigen value,Then characteristic equation is given…

Q: 4. Form the inner product to show that the operator du Lu rE (0, 1) %3D da? Bru = u(0) Bau = u'(1)…

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Q: In a rectangle, the width is one-third the length. The total perimeter is 40 inches. Find the length…

A: Solution: Given:    Width is one third of the length of rectangle     and the perimeter of rectangle…

Q: 2. Let A be an m x n matrix over complex field. (a) Prove that if x = N(L), then Ax is in both R(L)…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Define TE L(C²) by T(w, z) = (-z, w). Find the generalized eigenspaces corresponding to the distinct…

A: Given that the linear transformation T ∈ LC2 defined by…

Q: 7. The absolute norm for tensor of two eigenvectors of A = (23) is (b) √3 (c) 1/3 (a) 3 (d) None of…

A: Sol

Q: (ii) Prove that the product of matrices cos²0 Icos@sin0 cos@sin@] sin?e cos²p B = lcosøsing…

A: Given the matrix is A=cos2θcosθsinθcosθsinθsin2θB=cos2φcosφsinφcosφsinφsin2φ

Q: Prove that the function f = (sin kæ)(sin my)(sin nz) where: k, m, n are constants 82 + dx² ' Sy? '…

A: f(x) is an eigen function of an operator F(D) if  F(D)f(x)=kf(x),      where k is a constant, known…