SOLUTION: Hello, I'm trying to find the inverse of the following matrix; please help. I have to show all my work for homework, but I'm getting confused. Thank you! (18 9) (-8 -4)

Algebra ->  Matrices-and-determiminant -> SOLUTION: Hello, I'm trying to find the inverse of the following matrix; please help. I have to show all my work for homework, but I'm getting confused. Thank you! (18 9) (-8 -4)      Log On


   

Question 199607: Hello,
I'm trying to find the inverse of the following matrix; please help. I have to show all my work for homework, but I'm getting confused. Thank you!
(18 9)
(-8 -4)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix

To find the inverse of the matrix A=%28matrix%282%2C2%2C18%2C9%2C-8%2C-4%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C18%2C9%2C-8%2C-4%29%29 is abs%28matrix%282%2C2%2C18%2C9%2C-8%2C-4%29%29=0. So this means that d=0

Since the determinant is equal to zero, this means that no inverse exists.

Remember, the inverse of %28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29 is %281%2Fd%29%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29.

If d=0, then a division by zero occurs, which is NOT allowed.

So we can stop here.


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Answer:

So the inverse of A=%28matrix%282%2C2%2C18%2C9%2C-8%2C-4%29%29 does NOT exist since d=0 (ie the determinant is 0).