Chapter 4.2, Problem 9E

### 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

# In Exercises 1-42, use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand and others using technology. [HINT: See Examples 1-6.] x + y = 1 3 x − y = 0 x − 3 y = − 2

To determine

To calculate: The solution of the system of equations x+y=1,3xy=0,x3y=2 by the use of Gauss Jordan row reduction.

Explanation

Given Information:

The system of equation is,

x+y=13xāy=0xā3y=ā2

Formula Used:

Elementary row operations:

Type 1: Replacing the row Ri by aRi, where a is a nonzero number.

Type 2: Replacing the row Ri by aRiĀ±bRj, where a is a nonzero number.

Gauss Jordan reduction method:

Step 1: First, clear the fractions or decimals by using type 1 operation.

Step 2: Select the first nonzero element of the first row as pivot element.

Step 3: Use the pivot to clear its column using type 2 operation.

Step 4: Select the first nonzero element in the second row a pivot and clear its column.

Step 5: Turn all the selected pivot elements into a 1 using operations of type 1.

Calculation:

Consider the system of equation,

x+y=13xāy=0xā3y=ā2

The augmented matrix for the system of equations is,

[11131ā1ā30ā2]

Apply Gauss Jordan reduction method to get the solution of the given system of equation.

Begin by the selection of the first nonzero element of first row and clearing its column.

Perform the operations R2āR2ā3R1 and R3āR3āR1,

[11131ā1ā30ā2]ā[11100ā4ā4ā3ā3]

Next, pivot the first nonzero element of the second row and clear its column

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