Question 2. Ifø is a normalized fundamental matrix X = AX at to = 0 and if F is continuous in t, then * o(t - s)F(s) ds, is a particular solution of X = AX+F. Use the result above to find a general solution of 2 1 te²t 2 2t Xp(t): X = = .4 X +

Q: 3. Let (1 0 1 A = 10 -2 0 0-1 b = 0 f = f2 where f (a) Show that the matrix A is not asymptotically…

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Q: 3(4) 5 A = %3D -1 2

A: Here in the given question find the canonical form of the matrix A, which is P-1 A P = B   Find the…

Q: Consider f(t) = (cos t, sin t, t?) and g(x, y, z) = (x² + y² + z², 3x + 4y – 12z) and h = g(f(t)) =…

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Q: + Y are invertible matrices of the same size, then X(X¹+Y-¹) Y(X+Y)-¹ = 1.

A: One has to show the said property.

Q: Find a matrix A such that e [-] -2 is a solution for Ax= x'.

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Q: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

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Q: A matrix A is called orthogonal if A-1 = AT. (a) Show that if A is an orthogonal matrix then det(A)…

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Q: 2. (a) Let S= A 0 I B A, B & GL (R), B = B, A = (B n ¸ Check whether or not S SP2n(R). Also give an…

A: Here , I use latex to write the answer.

Q: 1. b) Find the Inverse of the matrix 1 2. 1 using Gauss-Jordan method. 1 1. 2]

A: Augment the given matrix with identity matrix. Apply row operations to convert given matrix into…

Q: Consider the matrix equation v' = [M°]v where 1( 4 3 M 3 8.5 and 1 510 3 8.5 )( 4 3 4 3 4 3 4 3 M10…

A: Hi! you have posted multiple subparts. As per norms, we will be answering only the first three…

Q: (a) Show that the 3 × 3 matrix p - (4) 1 1 >= is positive-definite for p > -1.

A: A  matrix is given as follows:

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

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Q: Suppose A is a 2 x 2 matrix. Show that the constant term of the characteristic equation |A – XI| = 0…

A: According to the given data, shows that the constant term of characteristic equation is equal to…

Q: Set up the 4 x 3 matrix E with E¡i = 0; = Vdi (the ith singular value) and all other Eij = 0.

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Q: = {[3] [7²]} and T = Let S and T be bases for R2, where S= and T=131-1 Find the change of base…

A: According to question,Given data,Let us assume s and T be bases for ℝ2,where,S = 13, -21T = 83, 47

Q: Find the inverse of the matrix, if x = 8' and y = 0 respectively. (1 1 x 1 2 -1 2 1 -1 (1 3 3 y 1 1…

A: Putting x=1 and y=0, the required matrix will be 1181 12-12 1-121 1330 We have to find the inverse…

Q: Question 1 Let f (W) be a function of vector W, i.e. 1 f(w) 1+e-wx Determine the first derivative…

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Q: 3. Compute the fundamental matrix and hence matrix exponential for each of these systems: 5 -3 (a)…

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Q: If Q is 3 x 2 matrix with orthonormal (:) 3 then 4 columns and a. ||Qx|| = 1 b. ||Qx|| = 25 O c.…

A: Option " d " is correct answer. Thankyou !

Q: O Consider a non-singular n x n matrix A. Let A = inf{||SA|| : A+ 8A is singular}. Show that 1 A…

A: We are given a non-singular n×n matrix A and ∆ = inf{||δA|| : A+δA is singular} And we have to show…

Q: 3 1.2 Given X = =[-³₁₁³] and Y = [-23 19]. 0 show that (X-Y)(X+Y) # x² - y²

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Q: 4. Let A be a 3 x 4 matrix and B be a 4 x 5 matrix such that ABx = 0 for all x E R°. a. Show that…

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Q: A² A³ - + 2! 3! Ife is defined as e¹=1+A+ X - 1⁰ *].0<x< Xx the functions f(x) and g(x). where A =…

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Q: [3 5 X1 Let T : R? → IR² be defined by T and X2 2 4 x2 {{}} 3 let B: Find the matrix |T|B. a11 a12…

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Q: 4 8. 5. Let C = 0. the cofactor matrix of a matrix A and let 7. -7 9] 611 b12 b13 A the inverse…

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Q: 2. Verify Calay-Hamilton theorem for the following matrix: (2 1 -1 A = (3 1 1 0 2

A: Solution:Given        A=21-1310102To findA-λI=0

Q: Consider the following matrix: A-() 1. Determine whether A is diagonalizable over C. If so,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 15. Given matrix N = Find the value of x such that NN' = 1, where I is -x the 2x2 identity matrix.…

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Q: If o is a normalised fundamental matrix of X = AX at to = 0 and f is continuous in t, then Xp(t) = |…

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Q: 2 Let B = then B is invertible and the function S : M2(R) → M2(IR) 8. defined by S(A) = BAB-1 is a…

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Q: 2. Assume that A is a 3 × 3 matrix such that for 1 - (³).. ), j = 2 1 I 0 ;). it holds that Az = (a)…

A: Introduction: If the transpose of a square matrix with real numbers or elements equals the inverse…

Q: This is a linear algebra/differential equations question (info in picture): Give an example of a…

A: A symmetric “A” is symmetric if,

Q: a. Suppose the vector x = and the symmetric matrix A = Show that for the quadratic form Q(x1,x2) =…

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Q: 5. Consider the matrix 11 -5 A = -2 10 (a) Compute the singular values for A (b) Compute the SVD for…

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