SOLUTION: Find the inverse of the matrix -1 6 0 -1

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Question 935785: Find the inverse of the matrix
-1 6
0 -1
Answer by MathLover1(20849) 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-1%2C6%2C0%2C-1%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C-1%2C6%2C0%2C-1%29%29 is abs%28matrix%282%2C2%2C-1%2C6%2C0%2C-1%29%29=1. So this means that d=1

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%28-1%29%2C6%2C0%2Chighlight%28-1%29%29%29 to get %28matrix%282%2C2%2Chighlight%28-1%29%2C6%2C0%2Chighlight%28-1%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C-1%2Chighlight%286%29%2Chighlight%280%29%2C-1%29%29 to get %28matrix%282%2C2%2C-1%2Chighlight%28-6%29%2Chighlight%280%29%2C-1%29%29

Step 4) Multiply by the inverse of the determinant



Multiply by 1%2Fd to get %281%2Fd%29%28matrix%282%2C2%2C-1%2C-6%2C0%2C-1%29%29

Plug in d=1 to get %281%29%28matrix%282%2C2%2C-1%2C-6%2C0%2C-1%29%29

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



Multiply 1 by EVERY element to get

Multiply to get %28matrix%282%2C2%2C-1%2F1%2C-6%2F1%2C0%2F1%2C-1%2F1%29%29

Reduce each element: %28matrix%282%2C2%2C-1%2C-6%2C0%2C-1%29%29


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Answer:

So the inverse of %28matrix%282%2C2%2C-1%2C6%2C0%2C-1%29%29 is %28matrix%282%2C2%2C-1%2C-6%2C0%2C-1%29%29

This means that if A=%28matrix%282%2C2%2C-1%2C6%2C0%2C-1%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C-1%2C-6%2C0%2C-1%29%29