Solve the following systems.(x +y +z = 11. {x + y – 2z = 3(2х + у +z%3D 2x + y – z = 02.{2х — Зу + z %3D 0х — 4у + 2z %3D 0-by Gaussian elimination method.

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Answered: Solve the following systems. x + y +z =…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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10.4 Solve the following system of equations using LU decompo- sition with partial pivoting: 2x, - 6x2 – x3 = -38 -3x - x2 + 7x3 = -34 -8x, + x2 - 2x3 = -20
Solve: 1] Use Gaussian Elimination Method. 2X + Y +Z = 4 0.1X - 0.1Y + 0.1Z = 0.4 3X + 2Y + Z = 2 X- Y+Z = 4 -2X + 2Y -2Z = - 8 2] Find the values of X, Y, and Z. (3+i)X - 3Y + (2+i)z = 3+4i 2X + Y- Z = 2+i 3X + (1+i)Y -4Z = 5+ 2i 3] Use determinants to find the values of X, Y, Z, W, N. 8X - 3Y + Z+ 5W - 4N = 21 5X + Y + 7Z - 13W + 15N = 27 7X + 3Y + 4Z - 18W - 12N = 35 11X - 7Y - Z+ 9w + 15N = 50 15X + 10Y - 7Z + 2W + 8N = 19 4] Find and solve the value of X in the equation: 5cosX = 4 - X
1. (a) Use definition of linear transformation to determine whether the transformation T:R? → R³ defined as follows is linear. -y T r+ 2y 2.r – 4y (b) Let T : R" → R" be a linear transformation. i. Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify. ii. Does S(0) = 0 mean that S is linear? If not, can you give a counter-example? (c) Consider the following matrix transformation T : R² → R² defined as a b T d i. If T rotates the 2D space 150° counter-clockwise, and then reflects the result across the new r-axis, find a, b, c, d. ii. What if T reflects the 2D space across the r-axis first and then rotates 150° counter-clockwise? Do you expect to get the same a, b, c, d? Why or why not?
Use Gaussian elimination method to find the solution to at least one of the given system of equations. 4. -5w + 2x + 3y - 7z 0 -w- 2x + y - 3z = 0 2w- 10x + 4y +4z 0 w-3x - 2y- 4z -0
Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x, y, and z in terms of the parameter t.) 3x + 3y + x + y + 2x + 5y + -x + 2y + (x, y, z) = 12z = 9 4z = 3 20z = 15 8z = 6
Find a solution, (x,y), of the following system of two nonlinear equations for which both x and y are real and strictly positive. g(x,y) = 4*x^2 + 5*x*y - 2 = 0 %3D h(x,y) = 9*y^2 + 3*x*y - 3 = 0 Such a solution exists. Report ONLY the x value. You must report your answer so that |your answer - correct answer| < 0.0001 to receive full marks. Do not use scientific notation when reporting your solution.
2. Find x, y and z using Gaussian elimination: x + 2y + 3z = 17 3x + 2y + z = 11 x − 5y + z = −5
3. Simple pulley system gives the equations X1 = T - g 2x2 = T – 2g X1 + x2 = 0 (a) Determine X1, X2 and T if g = 10 (b) Verify your solutions using Gaussian elimination
2. Solve the linear system algebraically. (2) / 2а — 3b — 5 { b = -1 -x + y= 2 (b) х — Зу 3 1 а — xị + 5x2 = 7 (c) 2.x1 – 7x2 = -3

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Solve the following systems. x + y +z = 1 1. {x + y – 2z = 3 2х + у +z %3D 2 x + y – z = 0 2.{2х — Зу + z%3D0 x – 4y + 2z = 0 by Gaussian elimination method.