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: 10.Solve the given (matrix) linear system: 1 21 [1 X' 13 %3D

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Q: √²³₁(−12xy² + 8x³y + 3)dxdy

A: LetWe have to evaluate the above integral.

Q: Below is a function f(a1,a2) = 2a13 + 3a22 + 3a12a2 - 24a2 over ℝ2 a.Determine all the stationary…

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Q: Express f in matrix notation where f(ū, 7) = 3x1Y1 – 2x2Y2 + 7x2Y2 – 8x2y3 + 4x3Y2 6x3Y3

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Q: Q4: Using Cayley - Hamilton theorem to find the inverse of the matrix A, where 1 1 2 A = 3 1 1 2 3 1

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Q: 4. Consider w = and v =. (a) Write z = as a linear combination of w and v. (1 2 3 (b) Consider the…

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Q: [11] a a Find the determinant of the following matrix: a a a b 2b X 3x 5y b 2x 3y b x 2y b X y N -Z…

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Q: 3. Find x such that the matrix A is equal to its own inverse. 2 -3 A %3D 3

A: Given :  The given matrix is   A = -2-33x To find : We have to find x such that the matrix A is…

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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Q: T a(x¹ B) ax

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Q: ( 7 ) to ( 2₁ ) ² -Y for M-1 makes sense geometrically. ? Find the inverse matrix of M and explain…

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Q: If the temperature at which a certain compound melts is a random variable with mean value 115°C and…

A: We have to solve given Questions.

Q: Give an example of a non-zero 2 × 2 matrix R which satisfics R² = 0. Suppose that M is an n x n…

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Q: Give the matrix associated with the quadratic form 10(x,)? – 5x,x2 +6(x,)².

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Q: The commutator [X. Y] of two matrices is defined by the equation [X. Y] = XY YX. Two anticommuting…

A: The matrices  A, B satifies the property A2=I, B2=I and A, B=2iC. The matrices A, B are…

Q: 13. Find an estimate for det (A) if A is an n × n matrix whose entries form some pattern of +10's

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Q: Determine the roots of the following function via matrix algebra: f(x) = sin x in the proximity of…

A: In order to determine the roots of the function in the proximity of , we will employ an iterative…

Q: For which real numbers x is the matrix [1x1 A = |01 x _10 1 invertible? For any such number x,…

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Q: Let y = 10 U₁ 11 -- and W = Span{u₁} a. Let U be the 2x1 matrix whose only column is u₁. Compute UTU…

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Q: If x=2:2:6, and y=[1, 3, 7]. Write the values of the matrix A=[x' y'] where ' is a matrix transpose.

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Q: Use the quotient law for tensors to show that the array -2xy -2xz /y²+z²-x² -2yx x²+z²-y² -2yz -2zx…

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Q: Give matrix A = (2  -1)                           (3     5).  and that h(T) =  and that h(T) =T² -…

A: See the attachment

Q: The matrix that projects onto the line y 1 is

A: We have to find the matrix that projects onto the line

Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

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