Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) x' Ax = sx? + 3.x3 + 2x3 – x1x2 + 8x2x3 to the standard form y P-lx, 1 -1/2 07 Q(y) = A137 + + 13y3, where A = -1/2 3 4 ... 4 2

Q: Verify Cayley-Hamilton theorem for the matrix A = and find its inverse. Also express A - 4A" 2 3 -…

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Q: Q2: (a) For given matrix A, find a 3 x 3 non-singular matrix P such that p-1AP is diagonal. A = |-3…

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Q: (-1 3 2 Find the polynomial of a square 3×3 matrix A=| 1 0 -2|given that -3 1 P(x) =14+19x– 3x² –…

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Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

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Q: We call g(x1, x₂) = ax² + 2bx1x2 + cx a quadratic form, a, b, c are constants. Suppose X1 X = try to…

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Q: Consider the quadratic form ƒ(x1, x2, x3) = x² + x² + 5x² + 2ax1x2 − 2x1x3 + 4x2x3 = x¹Qx

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Q: Use the following set of equ 2x1+ X2- X3 = -1 X2+ X3= 2 X1+ 2x2-X3=-1 Using Gauss-Jordan elimination…

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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: Find the determinant of the matrix M= -3-22¹ 8+22² +42³ 0 1+z²+2r³ 0 16+82² M-1- -8-42² and use the…

A: Please see the below picture for detailed solution.

Q: Given. Q(x)=3x² + x} +8x? –2x,x, –4.x,x3 Q(x)=x" Ax wher A is symmetric matrix 1 a, = a, = 3…

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Q: Consider the LP problem: Maximize 3xı + 2x2 subject to: x1 – x2 + 2x3 9 3x1 + x2 – x3 0 Find the…

A: Given LP problem is, x1-x2+2x3≤82x1+x2-x3≥6x1+3x2≥93x1+x2-x3≤10x1,x2,x3≥0 The canonical form of LP…

Q: 8 Consider a square matrix B whose inverse is given by B'. a In terms of B", what is the inverse of…

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Q: Let A be 3x5 matrix. Then AX=b has always infinitly many solutions.

A: Since not a particular question asked ,as per guidelines solution to first question is given below

Q: Q3:Solve Matrices by using (Gramer Rule ) 2X + 4Y - 2Z – 2 = 0 X + Z-3 =0 2X + Y- Z -1 = 0 Techn

A: Solve by crammer rule

Q: (b) Use the adjoint method to obtain the inverse matrix of P and hence. solve the system of linear…

A: Introduction: The transposition of the cofactor matrix for a given matrix is known as the adjoint of…

Q: Compute(Ax - y)||2, where A = Rm×n is a matrix and x ≤ Rª and y ≤ R™ are both vectors .

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Q: Determine whether the matrix A is positive-definite, negative-definite, positive-semidefinite,…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

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: Apply the conjugate gradient method to solve Ax = b = ones(lOO, 1), where A is the -1, 2, -1 second…

A: As per the question we have to implement the MATLAB Code for the conjugate gradient method in order…

Q: Use Cramer’s rule to solve for x, y & z matrix below   2x + y – z = 1 3x + 2y + 2z =13 4x -2y +…

A: 2x + y – z = 1  3x + 2y + 2z =13  4x -2y + 3z = 9

Q: [r(t)] [y(t)] What is the geometry matrix for this spline function? P(t) where x(t) = 2t3 + 3t2 – 6t…

A: The given spline function is, Pt=xtyt  where xt=2t3+3t2-6t+1  and  yt=3t3-4t2+3t-1 The geometry…

Q: and Y = (1 1 -) If X =0 1. Find the matrix Z where Y = Xiz %3D -2

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Q: Find the symmetric matrix that corresponds to the quadratic form q(x, y, z) = 3x² + 4æy – y² + 8xz

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Q: (c) Consider the quadratic form f(x1, x2, x3) = 3(a₁x₁ + a2x2 + a3x3)² = 4(b₁x₁ + b₂x2 + b3x3)². (i)…

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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: 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: 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: Find the coordinate matrix of w= 2-3x+x?+x vector relative to base B= {1, 1-x, (1-x)?, (1-x)³} in…

A: Given, w = 2 - 3x + x² + x³

Q: 4. Evaluate the determinant of the matrix by using a convenient column or row. (a) 3 -1 3 1 A = 2 0…

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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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Q: 2. Find the coordinate matrix of 7 = ³- {)-(-9)} B = 2 0 0 6 2 relative to the basis

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Q: 2. (a) Find the condition number of the coefficient matrix in the system (1761) (22) = (2²6) as a…

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Q: ах, - 3х, - 6х, -18 4.8х, - 4х, +7.2х, %3-16 а-9 3.2х, - 2х, -2.8х, %3D10

A: Let A be a square matrix. Apply Gauss elimination method, to find the LU decomposition of the matrix…