SOLUTION: Find the inverse matrix of : 1 0 -1 1 1 3 3 -2 1

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Question 1198415: Find the inverse matrix of :
1 0 -1
1 1 3
3 -2 1
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

You can do it using your calculator.


For instructions, use this video-lesson
https://www.youtube.com/watch?v=1yoja6phh3w


or this textual description
https://www.mathbootcamps.com/finding-the-inverse-of-a-matrix-with-a-ti83-or-ti84-calculator/


Or use online free-of-charge calculator www.reshish.com,
from which @MathLover1 copy-pasted her solution,
but did not provide the proper link to the source.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse matrix of :
matrix%283%2C3%2C%0D%0A1%2C+0+%2C-1%2C%0D%0A1%2C+1+%2C3%2C%0D%0A3%2C+-2%2C+1%29

Determinant is not zero, therefore inverse matrix exists.

Write the augmented matrix:


Find the pivot in the 1st column in the 1st row





Subtract the 1st row from the 2nd row




Multiply the 1st row by 3



Subtract the 1st row from the 3rd row and restore it




Find the pivot in the 2nd column in the 2nd row




Multiply the 2nd row by -2


Subtract the 2nd row from the 3rd row and restore it



Make the pivot in the 3rd column by dividing the 3rd row by 12




Multiply the 3rd row by -1


Subtract the 3rd row from the 1st row and restore it



Multiply the 3rd row by 4



Subtract the 3rd row from the 2nd row and restore it




There is the inverse matrix on the right