SOLUTION: Find the inverse for the given matrix: If [3 -8 ] [-3 -7] Then, A^-1=

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Question 255348: Find the inverse for the given matrix:
If [3 -8 ]
[-3 -7]
Then, 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%2C3%2C-8%2C-3%2C-7%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C3%2C-8%2C-3%2C-7%29%29 is abs%28matrix%282%2C2%2C3%2C-8%2C-3%2C-7%29%29=-45. So this means that d=-45

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%283%29%2C-8%2C-3%2Chighlight%28-7%29%29%29 to get %28matrix%282%2C2%2Chighlight%28-7%29%2C-8%2C-3%2Chighlight%283%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C-7%2Chighlight%28-8%29%2Chighlight%28-3%29%2C3%29%29 to get %28matrix%282%2C2%2C-7%2Chighlight%288%29%2Chighlight%283%29%2C3%29%29

Step 4) Multiply by the inverse of the determinant



Multiply by 1%2Fd to get %281%2Fd%29%28matrix%282%2C2%2C-7%2C8%2C3%2C3%29%29

Plug in d=-45 to get %28-1%2F45%29%28matrix%282%2C2%2C-7%2C8%2C3%2C3%29%29

Step 5) Multiply -1%2F45 by every element in the matrix (simplify and reduce if possible)



Multiply -1%2F45 by EVERY element to get

Multiply to get %28matrix%282%2C2%2C-7%2F-45%2C8%2F-45%2C3%2F-45%2C3%2F-45%29%29

Reduce each element: %28matrix%282%2C2%2C7%2F45%2C-8%2F45%2C-1%2F15%2C-1%2F15%29%29


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Answer:

So the inverse of %28matrix%282%2C2%2C3%2C-8%2C-3%2C-7%29%29 is %28matrix%282%2C2%2C7%2F45%2C-8%2F45%2C-1%2F15%2C-1%2F15%29%29

This means that if A=%28matrix%282%2C2%2C3%2C-8%2C-3%2C-7%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C7%2F45%2C-8%2F45%2C-1%2F15%2C-1%2F15%29%29