What would be the augmented mitrix ?

Question

Using Jordan-Gauss elimination on 3w-x=2y+z-4  ,what would be the augmented matrix ?

                                                  9x-y+z=10

                                                  4w+3y-z=7

                                                  12x+17=2y-z++6

Answer 1

In the augmented matrix, your first column will be all the coefficients of w, your second column will be all the coefficients of x, your third will be the coefficients of y, and your fourth will be the coefficients of z. The last column (the augmented part) will be the constant terms. We'll put every equation into the form aw + bx + cy + dz = e first. So:

 

3w - x - 2y - z = -4

0w + 9x - y + z = 10

4w + 0x + 3y - z = 7

0w + 12x - 2y + z = -11    (did you mean to have a w somewhere in there, instead of two constants?)

 

[3  -1  -2  -1  |  -4 ]

[0   9  -1   1   |  10]

[4   0   3  -1  |   7 ]

[0  12  -2  1  | -11]