b) Given a linear system as belowх — 2у + 3z %3 9,—х + Зу %3D — 4,2х — 5у + 5z %3D 17Find the value of x, y and z using gauss Jordan by completing the given matrix2 3193 51121-1

Answered: Image /qna-images/answer/0d339247-46c6-48fe-a428-08092ae6c50f.jpg

Answered: b) Given a linear system as below х —…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given the matrix A = 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ" Enter each matrix Q and D in the format [[a11 , a12 , a13] , [a21 , a22 , a23] , [a31, a32, a33]]. Note: if you need to enter a square root of a number x you can do it as follows: sqrt (x). Alternatively, you can compute matrix entries in the decimal form rounded to 3 decimal places, and enter them in this. Matrix Q: Matrix D:
Given a matrix 2x 1 0 3 -7 5 3xy + y² -1 -1 3 0 0 √√√xy-y² 0 1 -7 A = 00 Choose all values of x and y for which the given matrix A has a row echelon form (REF): 이 ○ 1 2 (x = 0, y = 1) O ○ (x = 0, y = 0) ° (x = 1/2 + x = 1/2 ) None of the others Given a matrix 1 2 A = 0 0 3x 1 0 105] 0 0 √8xy + y² 103 0 0 √√xy-y² 0 11 Choose all values of x and y for which the given matrix A has a reduced row echelon form (RREF): ° (x = 1/3₁ y = =/ ) " 3 ○ (x = 0, y = 1) 1 (x = 3 + x = 3) and (x = 0, y = 0) y |and (x = 0, y = 0) None of the others ○ (x=0, y=0)
2. For which h the matrix 1 1 -1 h 1 1 2 1 A 1 has two pivot columns?
c) For the 2x2 matrix C, find C-¹ by hand using C-1 = decadjC, where adj is the adjoint operator. 34 0 = [³4] 5 7
A) We calculate the unknowns vector {X} belonging to the above set of equations by using the Gaussian Elimination Method. solve it. Do your checks by putting the values you found in their place in the equation set. B) Find the determinant of the coefficients matrix
9. Given the bases B = {1+2t, 2+t} and C = {1-t, 2-3t} of P₁. Find the change of coordinates matrix Pc-B from B to C.
4
Given the following system of linear equations: Зх, + 4х, 1 2.x, 2х, + X3 -1. 2x, 2х, + 4х, (a) Describe v, A and b if the convention used is y. A = b. (b) Determine the linear transformation T that A represents by the convention (v)T = v · A. (c) Find the standard matrix A' of Tif the convention T(v) = A' -v is used instead.
If 3AT = 3 -6 2). then the a1,2 entry of the matrix A is

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b) Given a linear system as below х — 2у + 3z %3 9, —х + Зу %3D — 4, 2х — 5у + 5z %3D 17 Find the value of x,y and z using gauss Jordan by completing the given matrix 2 319 3 5 112 1 - 1