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please answer a-d, if you wont, then at least answer just for D only since its...
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 = 1 X1 - x2 + x3 = 3 - X1 + x2 + x3 = -1 a) (3 pts) Provide the Augmented matrix A for this system. b) (9 pts) Find the Row-Echelon Form (AREF) of the Augmented matrix. c) (2 pts) How many solutions does the system have? d) (6 pts) Based on the steps in part b), express Aref as a product...
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.
Mathematics IA Assignment 2 Semester 2, 2019 Algebra (a) You are given the following four linear equations: 2=2r4+4 -12-2-3r3, 124 x3. Write down a corresponding augmented matrix (b) A linear system has the following augmented matrix, 0 21 1 0-3 -1 2 5 (i) Use Gauss-Jordan elimination to bring the augmented matrix into reduced row echelon form. You must show your steps and, at each step, write down the elementary row operations that you are using. (ii) Hence write down...
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 equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution. Given the following system of linear equations 1. 2xi + 4x2...
The matrix given is in reduced echelon form 1 0 0 0 1 0-5 0 0 1 7 C 0 0 0 0 6. Write the system of equations represented by the matrix. (Use x as your variable and label each x with its corresponding column. Enter x_1 for x1, x_2 for x2, x_3 for x3, and x_4 for x4.) = 0 row 1 = 0 row 2 row 3 row 4 0 there is no solution, enter NO SOLUTION.)...
Sodium hydroxide (NaOH) reacts with sulfuric acid (H2S04) yields sodium sulfate (Na2S04) and water according to the following unbalanced equation To balance this equation, we need to find constants (xi, X2, X3, x4) in front of the products and the reactants to get the balanced equation in the form In order to get the values for x1, X2, .., x4, we compare the number of atoms of sodium (Na), oxygen (0), hydrogen (H), and sulfur (S) in the reactants with...
Problem 1. For the system of linear equations Ax- b, using elementary row operations on the augmented matrix, A is brought to row echelon form. The resulting augmented matrix is: 1 0 7 0 112 Row echelon form of (Alb-00 1 2 3 5 0 0 0 0 0 c (a) Find the rank and the nullity of A. Explain your answer. (b) For what values of c does the system have at least one solution? Explain your answer. (c)...
(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...
could you please help me with understanding why the answer to d) is not 3 parameters but instead 5,4 or 3? In a row echelon form, don’t we know that each non-zero rows has a leading 1 (by definition)? And so we know that the rank must be 3? 6-3=3 (by given theorem: n-r= #parameter) 4xy + 5ax2- 2ay +5x4 + 2xs 2x4+2xs 4x4 +x = 0 in ce 2x3- 9. (a) 2x, +2x- 4a x a + 2ax3 +...
Hi im struggling with part (b) and (c) of this linear algebra question. Any help would be greatly apprecated (a) Write down the augmented matrix corresponding to the system of linear equations: + 25 3w W W - + + y y + 1 Na + 4 [2 marks (b) For the remainder of this question the variables v, w, 2, y, and 2 will satisfy a system of linear equations whose augmented matrix is Ab). If the reduced row...