GJE with Rowops F09 O’Brien

How to Solve a System of Linear Equations Using Gauss-Jordan Elimination and the ROWOPS Program

Steps in Gauss-Jordan Elimination
Using ROWOPS / What You Do on the Calculator / What You Will See on the Calculator / What You Should Write on Paper
1 / Write the augmented matrix for the given
system of equations.
3x + y + 2z = 1
2x + 3y – 4z = –20
2x + 4y + 8z = 14 /
2 / Enter the matrix into your calculator.
a. Go to the Matrix Edit Screen
b. Enter the number of rows in the matrix
followed by the number of columns
c. Enter the matrix. Hit Enter after each input.
d. Carefully check each entry in the matrix
before you leave this screen. / Hit 2nd Matrix ► ► Enter
3 Enter
4 Enter /
3 / Select the ROWOPS program. / Hit PRGM
Select ROWOPS
Hit Enter
Hit Enter again to advance the program. /

4 / To get a one in a pivot position, multiply the pivot row by the reciprocal of the number in the pivot
position.
The row operation to get a one in the first pivot position, R1C1, isR1.
At every step, record on paper the row operations
followed by the resulting matrix.
If you cannot see the entire matrix, you can use the right arrow key (►) to reveal the 4th column. / Select 2 To Multiply
Hit Enter
1 Enter
1/3 Enter
► to see 4th column /
/ R1
5 / To get a zero above or below a pivot, take the opposite of the number you are trying to make zero times the pivot row and add it to the row you are
getting the zero in.
To get a 0 in R2C1, the row operation is –2R1 + R2.
To get a 0 in R3C1, the row operation is –2R1 + R3.
When pivoting on the calculator, only input the row number and the column number where the pivot one is located. / Hit Enter to advance prgm.
Select 3 To Pivot
Hit Enter
1 Enter
1 Enter
► to see 4th column /
/

6 / Column 1 is now in the proper form, so we are
ready to work on column 2.
First get a one in the new pivot position, R2C2, by multiplying row 2 by . / Hit Enter to advance prgm.
Select 2 To Multiply
Hit Enter
2 Enter
3/7 Enter
► to see 4th column /
/ R2
7 / Next get zeros above and below the pivot one.
To get a 0 in R1C2, the row operation is –R2 + R1.
To get a 0 in R3C2, the row operation is –R2 + R3. / Hit Enter to advance prgm.
Select 3 To Pivot
Hit Enter
2 Enter
2 Enter
► to see 4th column /
/
8 / Column 2 is now in the proper form, so we are
ready to work on column 3.
First get a one in the new pivot position, R3C3, by multiplying row 3 by . / Hit Enter to advance prgm.
Select 2 To Multiply
Hit Enter
3 Enter
7/100 Enter
► to see 4th column /
/ R3
9 / Next get zeros above and below the pivot one.
To get a 0 in R1C3, the row operation is –R3 + R1.
To get a 0 in R2C3, the row operation is R3 + R2. / Hit Enter to advance prgm.
Select 3 To Pivot
Hit Enter
3 Enter
3 Enter /
/
10 / The matrix is now in reduced row-echelon form.
Record the solution as an ordered triple. / Hit Enter to advance prgm.
To exit the program,
select 4 To Stop.
Hit Enter
Hit Clear
Hit 2nd On to turn the calculator off. / / Solution:
(–1, –2, 3)

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