Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row...
intersection in planes for the last three rows Write a system of linear equations and the row reduced echelon form (RREF) of the corresponding augmented matrix that meets the requirements described in the table. Ifno such system exists, state this and explain why. Intersects in a point No intersection Intersects in a line Intersects in a plane 2 equations 2 unknowns 2 equations 3 unknowns 3 equations 2 unknowns 3 equations unknowns Write at least 2 generalizations that can be...
(5 points) The following augmented matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations (using the variables X1, X2, and x3) or state that the system is inconsistent. (if a free variable is needed use the parameter t.) 1 0 3121 0 1 53 Lo 0 olo) con (10 points) Use row operations to compute the inverse of the matrix A = [ 53 -2] and use it to...
The augmented matrix of a system of linear equations has the following reduced echelon form. Use it to find the general solution of the system of equations 0 0 1 0 0 0 1 0 0 0 0 -1 5 -4 3 0 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0
1. For each of the following systems of linear equations, find: • the augmented matrix • the coefficient matrix • the reduced row echelon form of the augmented matrix • the rank of the augmented matrix • all solutions to the original system of equations Show your work, and use Gauss-Jordan elimination (row reduction) when finding the reduced row echelon forms. (b) 2 + 2x W 2w - 2y - y + y + 3z = 0 = 1 +...
Question 2 The augmented matrix of a system of linear equations has the following reduced echelon form. Use it to find the general solution of the system of equations 0 1 0 0 0 1 0 0 0 0 5 0 -4 -1 3 0 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0
3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has reduced row,echelon form given by 1401 0 01 -2 The general solution to this syste is (D) x = 1, y =-2, z = 0 (E) No solution 3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has reduced row,echelon form given by 1401...
6. The reduced row echelon form of a system of linear equations is shown below. Write the system of equations corresponding to the given matrix. Use x, y, and z as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. 1 0 41 41 0 1 3 2 Lo 0 0 0
20 1. This question deals with the following linear system of equations- 11 + 3.02 + x3 = 0 -4.x1 - 9:22 +2:03 = 0 (a) Write this system as a matrix equation Az = 7, and find the augmented matrix associated with this system. (b) Find the reduced row echelon form of the augmented matrix using elementary row operations. (c) Find the solution set for this linear system.
Consider the reduced row-echelon form of the augmented matrix of some system of linear equation in x1, x2, x3, x4, x5, x6 given by 1 0 0 0 -1 0 -16 0 1 0 0 -1 20 0 0 1 0 -1 1 1 1 12 0 0 0 1 -1 24 0 0 0 0 0 0 0 Suppose that the solutions satisfy the constrains x1 > 0, x2 > 0, X3 > 0, x4 > 0, X5 >...
Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution(s) to the system, if they exist. ſi 0 0 - - 1 0 1 0 - 5 0 0 1 | 10 0 0 0 - 10 (Note: The dotted vertical line in the matrix above should be a single vertical line.) a) Ox = 1, y =...