What is the inverse of this matrix?

Write the identity matrix beside the given matrix and then reduce the resultant matrix using the Gauss-Jordan method. The resulting matrix on the right will be the inverse.  I'll show you how to set it  up.

|   2 4  1 1 0  0 |

| -1  1  1  0 1 0 |

|   1  4  0  0 0 1|

Now, you need to do the Gauss-Jordan to get it in reduced row echelon form.

You can do this in two ways with a TI-84 or TI-84+ calculator.

Probably the most informative is to just put this matrix in your calc.  Then go to matrix and under MATH go down to rref( and press ENTER.  After that go to matrix and press ENTER to get rref([A] . Close the parentheses and press the MATH button and press ENTER. You should have rref([A])Frac.  Press ENTER, and you'll get the resulting matrix on your display screen.

If you don't have the Frac, you'll get repeating decimals. So,I definitely recommend using Frac if you use our calc.

You should have the following answer:

|1 0 0 4/9  -4/9   - 1/3|

| 0 1 0 -1/9 1/9     1/3|

| 0  0 1 5/9  4/9   -2/3|

It's a bummer to do by hand. Good luck.

formeng

long : augment the given matrix with the identity ; (1) subtract 3rd from 1st ; (2) add 1st and 2nd ; (3) subtract the 1st from 3rd ; (4) subtract  4 of the 2nd from the 3rd ; (5) multiply the 3rd by -1/9 ;

(6)subtract 3rd from the 2nd ; (7) subtract the 3rd from the 1st...the 'augment matrix is now the inverse

State here the procedures you saw to find such inverses. Then we will take it from there. 

Damnit! I was very good at it when we did it in math only a year ago, but I haven't had to do it since and now I forget how.