3: Let A € Mnxn. Define the matrix exponential as e4 k! k=0 eA is always convergent and A° = I. a) Let A be a diagonalizable matrix. Show that det(e^) = etr(A). %3D -1 1 b) Let B Find eB. 2

Q: The ODE (x dy/dx = yx²) is separable. true false If for a square matrix A and B, null matrix O, AB =…

A:

Q: Find cond1(A ) and cond∞(A). State whether th e given matrix is ill-conditioned.

A: The given matrix is A=1-2-36. To Find: cond1(A ) and cond∞(A) for the above matrix. To Check:…

Q: 8. Use the formula eAt = L-1 {(sI – A)-!}, to compute the matrix exponential for the matrix A =

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Q: 1 0 0 0 -1 -2 If [ B|1]=0 1 0 1 -2 1 where I is the ldentity matrix then B = %3D 0 0 1 -2 -2 0. 3.…

A: According to question,  B | I  = 100          0-13-23010          13-231001           02313

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: 3. 7. Compute the matrix exponential eAt for the diagonal matrix A = 0 4 8. Use the formula et = L-'…

A: According to rule of bartleby I can solve only 1dt question if you need another kindly repost it For…

Q: (b) Compute the matrix exponential function exp(-A) where [1 A = 2

A: The given problem is to find the exponential of the given matrix, We have to find the…

Q: Ouestoon = Find the inverse of the matrix with A'= Adj A A= -2

A: The objective is to find inverse of the given matrix using the given formula Given:

Q: (4) Given a matrix X of independent variables, psudo-inverse X† is defined as (X"X)-'x" (a) If X is…

A: If a matrix is of order (mXn) then transpose of A is of order (nXm).

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: Given A = 1 0 0 -3 1 1 1 - 2 -1 " x = and b = 300 150 400

A: Given that the system Ax=bHere A=1-3101-201-1 , b=300150400

Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: Let A = 52 (b) Find lim A". n→∞ | 312 716 9 4 54 (a) Find a matrix B so that B² = A.

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Q: Q/If you have the triple matrix below The inverse of matrix (A): 0.885 0.473 0.781 (A) = 2.047 0.973…

A: Sol:- 0.8850.4730.7812.0470.4780.1570.9730.8950.715-1Augment with a 3x3 identity…

Q: Homework : Find the inverse of the matrix and verify that A-'A = A A-1 = 1,

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Q: x₁ = 5x₁ - 4x₂ x₂ = 2x₁-x₂ Solve pansion. such that x₁ (0) = 1 and x₂ (0) = 2 by using the matrix…

A:

Q: A - (B U C) = %3D (А - B) U (A — С) (A – B) U C Option 1 Option 4 (А- В - С) (A – B) n (A – C)

A: given , A-(B∪C)  WE HAVE TO FIND EQUIVELENT TO IT FROM GIVEN FOUR OPTION

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: in

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Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

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Q: Table Q4(b) is generated from the function f(x)= e* – 4x² + B , where B is the last two digits of…

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Q: Find the LU composition of 1 | - matrix A =

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Q: Problem 3. Assume that A is a nx n real matrix. We define the exponential of A, as the series 1 e^ =…

A: Let A be any n×n real matrix then, eA=I+A+A22!+A33!+...    To Prove:  (a) If A=a00b then  eA=ea00eb.…