Chapter 4.2, Problem 60E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# If the reduced matrix of a consistent system of linear equations has five rows, two of which are zero, and seven columns, how many parameters does the general solution contain?

To determine

The number of parameters in the general solution of a consistent system of equations whose reduced matrix has 5 rows, 2 of which are zero and seven columns.

Explanation

Given Information:

A consistent system of linear equations, whose reduced matrix have 5 rows from which two are zeroes and has seven columns.

Consider a system of linear equations, whose reduced matrix has 5 rows from which two are zero and seven columns.

As there are seven columns in the reduced matrix there will be six unknowns as the last column if for the right hand sides of the equations.

Now there are 5 rows, 2 out of which are zeroes. This shows that there can be maximum three pivots one in each of the 3 rows left. These pivots have the three unknowns which cannot be the parameters.

For example,

Consider the given condition to form a reduced matrix,

[100000701<

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