document.write( "Question 175886: Find the inverse of each matrix if it exists. If it does not exist, write
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Algebra.Com's Answer #131002 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'll do the first two to get you started\r
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Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix

To find the inverse of the matrix \"A=%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29\", we can follow these steps:

Step 1) Find the determinant



The determinant of \"%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29\" is \"abs%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29=6\". So this means that \"d=6\"

Step 2) Swap the values



Now switch the highlighted values \"%28matrix%282%2C2%2Chighlight%286%29%2C2%2C3%2Chighlight%282%29%29%29\" to get \"%28matrix%282%2C2%2Chighlight%282%29%2C2%2C3%2Chighlight%286%29%29%29\"

Step 3) Change the sign



Now change the sign of the highlighted values \"%28matrix%282%2C2%2C2%2Chighlight%282%29%2Chighlight%283%29%2C6%29%29\" to get \"%28matrix%282%2C2%2C2%2Chighlight%28-2%29%2Chighlight%28-3%29%2C6%29%29\"

Step 4) Multiply by the inverse of the determinant



Multiply by \"1%2Fd\" to get \"%281%2Fd%29%28matrix%282%2C2%2C2%2C-2%2C-3%2C6%29%29\"

Plug in \"d=6\" to get \"%281%2F6%29%28matrix%282%2C2%2C2%2C-2%2C-3%2C6%29%29\"

Step 5) Multiply \"1%2F6\" by every element in the matrix (simplify and reduce if possible)



Multiply \"1%2F6\" by EVERY element to get

Multiply to get \"%28matrix%282%2C2%2C2%2F6%2C-2%2F6%2C-3%2F6%2C6%2F6%29%29\"

Reduce each element: \"%28matrix%282%2C2%2C1%2F3%2C-1%2F3%2C-1%2F2%2C1%29%29\"


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Answer:

So the inverse of \"%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29\" is \"%28matrix%282%2C2%2C1%2F3%2C-1%2F3%2C-1%2F2%2C1%29%29\"

This means that if \"A=%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29\" then \"A%5E%28-1%29=%28matrix%282%2C2%2C1%2F3%2C-1%2F3%2C-1%2F2%2C1%29%29\"

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\n" ); document.write( "\n" ); document.write( "In order to find the inverse of \"%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C2%2C1%2C1%2C1%2C1%29%29\", we need to find the row reduced form of \r
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\n" ); document.write( "\n" ); document.write( "This solution was generated by the Linear Algebra Toolkit\r
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\n" ); document.write( "\n" ); document.write( "Notice how the right hand matrix is \"%28matrix%283%2C3%2C-1%2C-1%2C4%2C1%2C2%2C-5%2C0%2C-1%2C2%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "So this means that the inverse of \"%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C2%2C1%2C1%2C1%2C1%29%29\" is \"%28matrix%283%2C3%2C-1%2C-1%2C4%2C1%2C2%2C-5%2C0%2C-1%2C2%29%29\"\r
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