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Reduced Row Echelon Form in Excel
In this example, we want to utilize Excel to solve the system
4
2
5
11
2
2
3
2
14
x
y
z
x
y
z
x
y
z

Start by converting this system to an augmented matrix,
4
2
5 11
1
1
1
2
2
3
2
14
To put a matrix in reduced row echelon form in Excel, we carry out the row
operations using the unique capabilities of Excel.
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Reduced Row Echelon Form in Excel
Put in the Original Matrix
1. Start Excel. Excel is a spreadsheet program that contains a huge table with many
unique capabilities. The table is labeled by column and row with letters and numbers.
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Reduced Row Echelon Form in Excel
2. The cell called A1 is the cell in the
column labeled A and the row labeled 1.
Click your cursor in that cell and type a 4,
the first entry in the augmented matrix for
the system.
3. The cell beneath A1 is labeled as A2
since it is in the A column and second
row. Click your cursor in that cell and
type a 1. Continue typing in the entries in
the augmented matrix until they appear
like those pictured to the right.
4. In the cell labeled E1, type the words
Original Matrix. Just above this entry,
click on the column border. While holding
the right mouse button, stretch it to make
it wider.
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Reduced Row Echelon Form in Excel
5. Click in cell E1 and then the Align Text
Right button,
, from the Alignment
Panel. This will move the text to the right
side of the cell. As we proceed through
the steps below, we’ll use a similar style
to document the row operations for each
step.
6. Click in cell A2. While holding the left
mouse, drag the mouse to cell D2 so that
cells A2 through D2 are selected.
7. From the Clipboard Panel, select Copy.
This copies the second row into the
clipboard.
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Reduced Row Echelon Form in Excel
8. To paste this row into the first row of a
new matrix, click in cell A5.
9. From the Clipboard Panel, locate the
Paste button. Click on the down arrow
under the word Paste. From the menu
that appears, click on Paste Values. This
will paste the second row of the original
matrix into cells A5 through D5.
10.  Repeat steps 6 through 9, but paste
the first row in place of the second row.
11.  Repeat steps 6 through 9 and paste
the third row into the new matrix as the
third row. The new matrix should look like
the 1 to the right.
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Reduced Row Echelon Form in Excel
12.  Now that there is a 1 in the first row,
first column, we must use row operations
to put 0’s below it. The first row will not
change in the new matrix so select cells
A5 through D5 by drag clicking these
cells. Press Copy from the Clipboard
Panel.
13.  Click your mouse in cell A9. From the
Clipboard Panel, locate the Paste button.
Click on the down arrow under the word
Paste. From the menu that appears, click
on Paste Values. This pastes the first row
into the new matrix unchanged.