SOLUTION: Determine whether the matrix has an inverse. If an inverse exists, find it. -1 - 1 2 3

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Question 116768: Determine whether the matrix has an inverse. If an inverse exists, find it.
-1 - 1
2 3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A=%28matrix%282%2C2%2C-1%2C1%2C2%2C3%29%29
A matrix has an inverse if its determinant is not equal to zero.
For a 2x2 matrix,
A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29
The determinant is abs%28A%29=ac-bd
In this case the determinant is
abs%28A%29=ac-bd=%28-1%29%283%29-%28-1%29%282%29
abs%28A%29=-3%2B2
abs%28A%29=-1
The inverse of a 2x2 matrix is given by,
A%5E%28-1%29=%281%2Fabs%28A%29%29%2A%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29
In this case
A%5E%28-1%29=%281%2Fabs%28A%29%29%2A%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29
A%5E%28-1%29=%281%2F-1%29%2A%28matrix%282%2C2%2C3%2C1%2C-2%2C-1%29%29
A%5E%28-1%29=%28matrix%282%2C2%2C-3%2C-1%2C2%2C1%29%29