SOLUTION: Find the inverse of the matrix if it exists.? A= [1,-2] [1,2] A^-1=

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Question 627192: Find the inverse of the matrix if it exists.?
A=
[1,-2]
[1,2]
A^-1=
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%2C1%2C-2%2C1%2C2%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C1%2C-2%2C1%2C2%29%29 is abs%28matrix%282%2C2%2C1%2C-2%2C1%2C2%29%29=4. So this means that d=4

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%281%29%2C-2%2C1%2Chighlight%282%29%29%29 to get %28matrix%282%2C2%2Chighlight%282%29%2C-2%2C1%2Chighlight%281%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C2%2Chighlight%28-2%29%2Chighlight%281%29%2C1%29%29 to get %28matrix%282%2C2%2C2%2Chighlight%282%29%2Chighlight%28-1%29%2C1%29%29

Step 4) Multiply by the inverse of the determinant



Multiply by 1%2Fd to get %281%2Fd%29%28matrix%282%2C2%2C2%2C2%2C-1%2C1%29%29

Plug in d=4 to get %281%2F4%29%28matrix%282%2C2%2C2%2C2%2C-1%2C1%29%29

Step 5) Multiply 1%2F4 by every element in the matrix (simplify and reduce if possible)



Multiply 1%2F4 by EVERY element to get

Multiply to get %28matrix%282%2C2%2C2%2F4%2C2%2F4%2C-1%2F4%2C1%2F4%29%29

Reduce each element: %28matrix%282%2C2%2C1%2F2%2C1%2F2%2C-1%2F4%2C1%2F4%29%29


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Answer:

So the inverse of %28matrix%282%2C2%2C1%2C-2%2C1%2C2%29%29 is %28matrix%282%2C2%2C1%2F2%2C1%2F2%2C-1%2F4%2C1%2F4%29%29

This means that if A=%28matrix%282%2C2%2C1%2C-2%2C1%2C2%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C1%2F2%2C1%2F2%2C-1%2F4%2C1%2F4%29%29