SOLUTION: PLease find the inverse of the matrix -9 5 6 -3

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Question 262917: PLease find the inverse of the matrix
-9 5
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%2C-9%2C5%2C6%2C-3%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C-9%2C5%2C6%2C-3%29%29 is abs%28matrix%282%2C2%2C-9%2C5%2C6%2C-3%29%29=-3. So this means that d=-3

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%28-9%29%2C5%2C6%2Chighlight%28-3%29%29%29 to get %28matrix%282%2C2%2Chighlight%28-3%29%2C5%2C6%2Chighlight%28-9%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C-3%2Chighlight%285%29%2Chighlight%286%29%2C-9%29%29 to get %28matrix%282%2C2%2C-3%2Chighlight%28-5%29%2Chighlight%28-6%29%2C-9%29%29

Step 4) Multiply by the inverse of the determinant



Multiply by 1%2Fd to get %281%2Fd%29%28matrix%282%2C2%2C-3%2C-5%2C-6%2C-9%29%29

Plug in d=-3 to get %28-1%2F3%29%28matrix%282%2C2%2C-3%2C-5%2C-6%2C-9%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%2C-3%2F-3%2C-5%2F-3%2C-6%2F-3%2C-9%2F-3%29%29

Reduce each element: %28matrix%282%2C2%2C1%2C5%2F3%2C2%2C3%29%29


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Answer:

So the inverse of %28matrix%282%2C2%2C-9%2C5%2C6%2C-3%29%29 is %28matrix%282%2C2%2C1%2C5%2F3%2C2%2C3%29%29

This means that if A=%28matrix%282%2C2%2C-9%2C5%2C6%2C-3%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C1%2C5%2F3%2C2%2C3%29%29