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Chapter 11: Q. 27 (page 729)

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1, x2, x3, x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.

100|1010|2000|3

Short Answer

Expert verified

The system of equation is x=1,y=2,0=3and the system is inconsistent

Step by step solution

01

Step 1. Given Information  

The given matrix is

100|1010|2000|3

02

Step 2. Explanation  

The given matrix has three rows. So, it represents a system of three linear equations. The 3 columns to the left of vertical bar indicate that the system has three variables.

Let the variables be x ,y and z. Then system of linear equation corresponding to the given matrix is as follows,

x=1,y=2,0=3

A system of linear equation is said to be consistent when it has at least one solution otherwise it is inconsistent.

So, the system is said to be inconsistent because the last equation of the system has no solution.

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