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(Solved): Find A1, or explain why it does not exist. A=127111114 ...






Find \( A^{-1} \), or explain why it does not exist.
\[
A=\left[\begin{array}{rrr}
1 & 1 & 1 \\
2 & 1 & -1 \\
7 & 1 & -4
\end
Find , or explain why it does not exist.


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Consider the matrix
  


To determine if the inverse of matrix    exists, we can calculate the determinant of matrix   . If the determinant is non-zero, then the inverse exists; otherwise, it does not exist.


The determinant of matrix    can be found as follows:
  
  

Since the determinant is non-zero, the inverse exists.
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