The matrix A
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.):
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.
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
Multiply row 2 by –1/8: 8\Y2 @RCI!
Multiply row 2 by 6 add it to row 3, replacing it: 6#2#3 @RCIJ!
Next, perform the following row