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Solving Systems Using Matrices

What will happen if we try to find this guy's inverse?

[ row 1: 1 , 3 row 2: 2 , 6 | row 1: 1 , 0 row 2: 0 , 1 ]

STEP 1:

-2 times Row 1 ... [ row 1: -2 , -6 row 2: 2 , 6 | row 1: -2 , 0 row 2: 0 , 1 ]


 

Row 1 back to normal

Row 1 +
Row 2

[ row 1: 1 , 3 row 2: 0 , 0 | row 1: 1 , 0 row 2: -2 , 1 ]

Getting zeros in both spots here means we are dead in the water!  No matter what we try, we won't be able to turn the left side into the identity matrix.

Hey, do you remember what happened when the determinant of the coefficient matrix = 0 when we were solving systems using Cramer's Rule?

x + 3y = 8

2x + 6y = 5