must use Gaussian Method AND Cramers rule!! PLEASE HELP!

Question

1) 3x-2y+z=9

    x+y+4z=4

   2x+3z=-1

 

 

 

2) x-2y=5z+4

   6y+18z=2x-8

  -3x+8y+20z=-18

 

 

 

 

3) -14=-20y-7x

     10y+4=2x

 

Answer 1

Here's how to do problem 2 using Cramer's rule. 

Create matrix B on the calculator, containing 3 columns (coefficients of x, y, x) and 3 rows (three equations):

1  -2  -5

-2  6  18

-3  8  20

then det([B]) = -6  <--this is the value of the System Determinant, D.

 

Now edit [B] to put the right hand side constants only in place of the x-column coefficients:

4  -2 -5
-8  6 18
-18 8 20
then det([B]) =12.  <--this is the value of the determinant Dx

So the value of x = 12/-6 = -2.        [x = D_x / D].

Now edit [b] to contain these data,:

1  - 4-  5
-2  -8  18
-3 -18  20
then det([B]) = 48  <-- D_y.  The value of y = D_y / D so y =48 / -6 = -8.

Finally, create the matrix [B] in which the right-side constants are substituted for the column of "z" coefficients:

1 -2  4
-2 6 -8
-3 8 -18
then det([B]) = -12 <--D_z.  So z = D_z / D = -12 / -6 = 2.

Solution: (-2, -8, 2)

[verified using rref command on 3 by 4 Augmented Matrix for this system]