SOLUTION: Find the inverse of the matrix 9 -4 -6 3

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Question 875437: Find the inverse of the matrix
9 -4
-6 3
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%2C9%2C-4%2C-6%2C3%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C9%2C-4%2C-6%2C3%29%29 is abs%28matrix%282%2C2%2C9%2C-4%2C-6%2C3%29%29=3. So this means that d=3

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%289%29%2C-4%2C-6%2Chighlight%283%29%29%29 to get %28matrix%282%2C2%2Chighlight%283%29%2C-4%2C-6%2Chighlight%289%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C3%2Chighlight%28-4%29%2Chighlight%28-6%29%2C9%29%29 to get %28matrix%282%2C2%2C3%2Chighlight%284%29%2Chighlight%286%29%2C9%29%29

Step 4) Multiply by the inverse of the determinant



Multiply by 1%2Fd to get %281%2Fd%29%28matrix%282%2C2%2C3%2C4%2C6%2C9%29%29

Plug in d=3 to get %281%2F3%29%28matrix%282%2C2%2C3%2C4%2C6%2C9%29%29

Step 5) Multiply 1%2F3 by every element in the matrix (simplify and reduce if possible)



Multiply 1%2F3 by EVERY element to get

Multiply to get %28matrix%282%2C2%2C3%2F3%2C4%2F3%2C6%2F3%2C9%2F3%29%29

Reduce each element: %28matrix%282%2C2%2C1%2C4%2F3%2C2%2C3%29%29


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Answer:

So the inverse of %28matrix%282%2C2%2C9%2C-4%2C-6%2C3%29%29 is %28matrix%282%2C2%2C1%2C4%2F3%2C2%2C3%29%29

This means that if A=%28matrix%282%2C2%2C9%2C-4%2C-6%2C3%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C1%2C4%2F3%2C2%2C3%29%29