11: Given the function f(x) = 8x² - 4x₁x₂ + 5x² and Xo = [5 2]. Then G¹g at Xo is equal (( G is the Hessian matrix and g is the gradient vector for f(X))) A: [25] B: [-2 -5] C: [5 2]T D: [-5 -2]T A B C D

Q: Let B = matrix from B to C 8 - { }], ] } and c-{[7], [43]} C = be two bases for R². Find the change…

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Q: Find the inverge of the 2x2 matrix Cos t Sin t - Sine Cose

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Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

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Q: 3. Let B = {[4] [7]} and c={[7][7]} 4 9 C a. Find the change of coordinate matrix from C to B.

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Q: Q6. Consider the function f: R³ R² defined by f((x, y, z))= (-2r, y + 32). (a) Show directly that f…

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Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Use the given definition to find f(A): If f(x) = a, + a,x + a,x2 + ... + a,x" is a polynomial…

A: We have to find f(A).

Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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Q: Compute the quadratic form x¹Ax for the given matrix A and vector x. [59 0] A = 91 4, X = X2 04-2 x3…

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Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

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Q: Consider the following function; Q(x1, x2, X3) = 2x? + 3x? – xž + 5x1x3 + x2x3 Find the matrix A…

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Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: Let B = {b1,b2} and C = {c1, C2} be R². Produce the change-of-coordinate matrix from B to C and from…

A: The change of basis matrix form B to C (or from the basis B to the basis C ) and C to B where B and…

Q: 2. Write the following functions in matrix form: (a) f(x1,x2, X3) = (x1 + 2x3, x1 + 3.x2 – x3, x1)…

A: Given the function is a fx1,x2,x3=x1+2x3, x1+3x2-x3, x1 In a matrix form…

Q: Let A be a 2 x 2 matrix a If ad – bc + 0, then A-1 ad-be ad-be ad-e ad-be. such that [1 AA-1 = A-'A…

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Q: and (96) = C1 A₁-3+4i with ₁ = Write the solution to the linear system [+] in the following forms.…

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Q: x 2y * (()) = (2+²) 4x 3. Let T a) T can also be written as T I ((₁)) = 4(3) A b. matrix you found…

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Q: Let z be a real number and let A be the matrix 2 I A - (-34). -2 i. Find all values of r such that A…

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Q: For the matrixA=daig(-2,-1,2), put the following values in increasing order: det(A), rank(A),…

A: The given matrix is,  A = diag(-2, -1, 2). We have to put the following quantities in increasing…

Q: Each of J, K, L, M and N is a linear transformation from R? to R². These functions are given as…

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Q: If X and Y are two full column-rank matrices of rank p, find all matrices A for which R(A) = R(X)…

A: Here given that are two column rank matrices of rank  so that where .Obviously  .From above…

Q: Show that if two real symmetric matrices A, B are congruent then there is a linear change of…

A: The objective of this question is to prove that if two real symmetric matrices A and B are…

Q: Consider the following. B = {(0, -1, -2), (4, 1, 2), (12, 3, 7)}, B' = {(−3, −2, −6), (2, 1, 3), (2,…

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Q: se the above equation is expressed as Ax = b with x = uations in one matrix form as (Alb)= -10 -10…

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Q: For each of the following quadratic forms, write down the symmetric coefficient matrix A such that Q…

A: According to Guidelines only  first there subparts can be solved.

Q: Let f(u, v) = (u - v, 1,u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first…

A: As per our guidelines we are answer submit of only first three sub parts question of multiple sub…

Q: Find the matrix for T(~) = projów where v =[−4 −8 −6]ª.

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