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A linear system with no free variables: Consider the linear system Xị + 2x2 + 33 = 115 2x1 – x2 + 3x3 = 1421 4x1 – x2 + 12x3 = 4214 You'll solve this linear system in a few ways: (a) First, enter the coefficient matrix for this system as the variable “A", and the right- hand side as the column vector "b". Next, enter the command "A \ b", which outputs the (in this case, unique) solution to this linear system. (b) (*) Second, enter the augmented matrix as the variable “M". In the next line, run the command rref (M), which outputs the row reduced echelon form of M. Note that there are no free variables. Explain, in words, why in this case we have that the last column of M is the (unique) solution to the original linear system. If you did everything right, you should find that this solution is the same as that you found in part (a).

A linear system with no free variables: Consider the linear system Xị + 2x2 + 33 = 115 2x1 – x2 + 3x3 = 1421 4x1 – x2 + 12x3 = 4214 You'll solve this linear system in a few ways: (a) First, enter the coefficient matrix for this system as the variable “A", and the right- hand side as the column vector "b". Next, enter the command "A \ b", which outputs the (in this case, unique) solution to this linear system. (b) (*) Second, enter the augmented matrix as the variable “M". In the next line, run the command rref (M), which outputs the row reduced echelon form of M. Note that there are no free variables. Explain, in words, why in this case we have that the last column of M is the (unique) solution to the original linear system. If you did everything right, you should find that this solution is the same as that you found in part (a).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...
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2. A linear system with no free variables: Consider the linear system X1 + 2x2 + 3x3 = 115 2x1 x2 + 3x3 = 1421 4x1 x2 + 12x3 = 4214 %3D You'll solve this linear system in a few ways: (a) First, enter the coefficient matrix for this system as the variable "A", and the right- hand side as the column vector "b". Next, enter the command "A \ b", which outputs the (in this case, unique) solution to this linear system. (b) (*) Second, enter the augmented matrix as the variable "M". In the next line, run the command rref (M), which outputs the row reduced echelon form of M. Note that there are no free variables. Explain, in words, why in this case we have that the last column of M is the (unique) solution to the original linear system. If you did everything right, you should find that this solution in part (a). the same as that you found
Transcribed Image Text:2. A linear system with no free variables: Consider the linear system X1 + 2x2 + 3x3 = 115 2x1 x2 + 3x3 = 1421 4x1 x2 + 12x3 = 4214 %3D You'll solve this linear system in a few ways: (a) First, enter the coefficient matrix for this system as the variable "A", and the right- hand side as the column vector "b". Next, enter the command "A \ b", which outputs the (in this case, unique) solution to this linear system. (b) (*) Second, enter the augmented matrix as the variable "M". In the next line, run the command rref (M), which outputs the row reduced echelon form of M. Note that there are no free variables. Explain, in words, why in this case we have that the last column of M is the (unique) solution to the original linear system. If you did everything right, you should find that this solution in part (a). the same as that you found
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