SOLVE STEP BY STEP IN DIGITAL FORMAT Consider the function 5 5 f(x, y) In(x + yo) = defined on the interior of the first quadrant of R². Is it a concave or convex function? Is it strictly? Justify your answer in terms of the Hessian matrix.

Q: 1. Calculate exp(A) where A is the 2×2 matrix given by A 7 -2 -[33] = 5 5

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Q: For back substitution with a band matrix (width w ), show that the number of multiplications to…

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Q: Solve the wave equation u,- c u = xt, 0 0, cisa constant subject to boundary conditions u(0,1) = t…

A: The boundary conditions are The initial conditions are Let the solution be

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: [x__3y] [x_2y_ 9. Find the inverse of the matrix:

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Q: If X is an unknown matrix And A and B are known : [A]×[x]=[B]_ 5x5 5×1 [x] = ?

A: Given matrix A is of order 5×5 and matrix B of order 5×1 and A5×5×x=B5×1 We have to find the matrix…

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: Use this formula to compute the inverse of the matrix [i 0 2] A = 2 2 3 li i i] Check your result by…

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Q: Example: f=(f¹, f²): R³ → R² (-6) T1I2X3 that is, f¹(x) = x₁²² and ƒ²(x) = 1₁T2Tz. Then the Jacobi…

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Q: E = 5 -2 -4 3 2 2 -4 -4 -4 0 -3 2 3 2 4 4 -2

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Q: Solve for the matrix X eMz (R): -2 3 ļ s X = 7|o

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Q: Find the singular values the matrix:

A: Given:A=1201-21Singular values:detATA-λI=0

Q: f is represented by the matrix: A = (0 2) (7 8) Show that f is invertible and find the…

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Q: T a(x¹ B) ax

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Q: 1.19 Assume that h: R² R³ is determined by this action. (1) - (9). 2 Using the standard bases, find…

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Q: Jse Use the following set of equations to solve questions (7,8, :9, 10, 11, 12) based on Gauss…

A: Given : 2x1+x2-x3=23x1-2x2+x3=1x1-2x2+2x3=-1` The above system of equations can be written in matrix…

Q: f = -x² - y² + 2xy. Diagonalize the quadratic form, i.e., find an orthogonal matrix P such that the…

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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: 5) Find dx/dt of Matrix: X 5e-1 2e-¹ -7e-t

A: We know , d/dx(e-t) = -e-t   Given X = 5e-t2e-t-7e-t

Q: 3 Construct a 3 x 3 nonzero matrix A such that the vector 2 is a solution of Ax = 0. A = [(1,2,3),…

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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: 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: Consider the quadratic form: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not…

A: Step 1:Step 2:Step 3:Step 4:

Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

A: Given :                    2-134-32321 To find :                 The cofactors for C13 , C22 , C32…

Q: Write an Octave function that implements Choleski's method. The input must be a positive definite…

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

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

Q: The matrix that projects onto the line y = 1 2 8 is X 0.6 0.8 0.8 -0.6

A: Let  be projection on the line Then  is  a linear transformation with matrix

Q: Matrix AA is transformed by a scalar to form matrix BB . A=[−1.5   3]       B=[3   −6] [4.25…

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Q: Use Use the following set of equations to solve questions (7,8, :9, 10, 11, 12) based on Gauss…

A: We have to find value of R2 after using transformation:

Q: find the standard matrix for the reflection of IR squared about the line that makes an angle of π/4…

A: Consider line that makes an angle of  with positive  axis.To illustrate the standard matrix for…

Q: Q6: Solve for matrix X in the matrix equation X- A" = 21, where I is a unit matrix with size 2 x 2…

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