Page 11-32
To obtain a solution to the system matrix equation using Gaussian elimination,
we first create what is known as the augmented
matrix corresponding to A, i.e.,
The matrix A
aug
is the same as the original matrix A with a new row,
corresponding to the elements of the vector b, added (i.e., augmented) to the
right of the rightmost column of A.
Once the augmented matrix is put together, we can proceed to perform row
operations on it that will reduce the original A matrix into an upper-triangular
matrix. For this exercise, we will use the RPN mode (H\@@OK@@), with system
flag 117 set to SOFT menu. In your calculator, use the following keystrokes.
First, enter the augmented matrix, and make an extra copy of the same in the
stack (This step is not necessary, except as an insurance that you have an extra
copy of the augmented matrix saved in case you make a mistake in the forward
elimination procedure that we are about to undertake.):
[[2,4,6,14],[3,-2,1,-3],[4,2,-1,-4]] ``
Save augmented matrix in variable AAUG: ³~~aaug~ K
With a copy of the augmented matrix in the stack, press „´ @MATRX! @ROW! to
activate the ROW operation menu. Next, perform the following row operations
on your augmented matrix.
Multiply row 1 by ½: 2Y 1 @RCI!
Multiply row 1 by –3 add it to row 2, replacing it: 3\ # 1 #2
@RCIJ!
Multiply row 1 by –4 add it to row 3, replacing it:
4\#1#3
@RCIJ!
.
4
3
14
,,
124
123
642
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
−= bxA
Z
Y
X
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
−
−
−=
4
3
14
124
123
642
aug
A
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