Solve Inverse Matrices: 2x2, 3x3, and More - Easy Steps!

[CRTNY]

#1)2 4
6 -4

#2) 1 4
-2 -8

#3) 3 1
0 2

#4) 1 5 6
2 1 1
0 -4 -8

 

[Hurkyl]

What's confusing?

 

[CRTNY]

how to do the actual inverses...when it comes to the Gauss-Jordan method...i get lost

 

[CRTNY]

these problems are due by 2 tomm

 

[Hurkyl]

Well, where do you get lost?

 

[CRTNY]

once you set up the equation (for example #1) to 2x+4z=1
6x+-4=0

and go on to set up 2 4| 1 0
6 -4| 0 1

...I don't know what to do from here...this step is where the Gauss-Jordan method comes in...and I don't know how to set up the Row equation...

 

[Hurkyl]

Why are you talking about equations? When doing Gaussian elimination, you do nothing but row operations a matrices.

 

[CRTNY]

thats what i am referring to...

 

[triden]

When doing GJ the method is to make the first row, first column a 1, and then 0's in the rest of the rows in that column. Since there is a 2 in R1 C1, you would take 1/2 R1 to make the two a one. Then you have to make the 6 a 0, so you would go: R2 - 6R1 (to get rid of the 6)

Now your matrix is:

1 2 | 1/2 0
0 -10 | -3 1

or something like that. Now make the -10 a 1 and make the two a 0 after that. Then the right hand side will be your inverse. There is an easier way of finding inverses for a 2x2 matrix using inverses though.