Perform Gauss-Jordan elimination on the following augmented matrix. (please help .....iam stuck?

Question

Perform Gauss-Jordan elimination on the following augmented matrix.

[ 3 -4 I 2 ]
[ 0 -1 I 7 ]
[ 3/2 -2 I 1 ]

Answer 1

I assume you remember your elementary row operations:

[ 3, -4 I 2] divide this row by three
[ 0, -1 I 7]
[ 3/2, -2 I 1] subtract 1/2 row 1

[1, -4/3 | 2/3] subtract 4/3 row 2
[0, -1 | 7] multiply this row by -1
[0, 0 | 0]

[1, 0 | -26/3]
[0, 1 | -7]
[0, 0 | 0]

So this system of equations is consistent, and has the unique solution x=-26/3, y=-7

Answer 2

this is b a million*x + 0*y -3*z = 6 0*x + a million*y +2*z = 7, so the proposed answer satisfies the equations. The 3x3 matrix (the left component 3 columns of your matrix) is obviously singular (the final row is all zeros), meaning you have greater unknows (levels of freedom) than equations (constraints). The rank of your 3x3 matrix is two, you have 3 columns, so which you're loose to set one in all your variables (e.g. x), although you like it, and nevertheless set the different 2 (y and z) to fulfill the equations. a third one (y)