My Math Forum Matrix A^-1 to find A

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 February 6th, 2012, 09:17 AM #1 Newbie   Joined: Nov 2010 Posts: 3 Thanks: 0 Matrix A^-1 to find A (tA)^-1 = row 1 = [2, 7] row 2 = [0,9] How do I find A?
February 6th, 2012, 07:22 PM   #2
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Re: Matrix A^-1 to find A

Quote:
 Originally Posted by Nexusfactor (tA)^-1 = row 1 = [2, 7] row 2 = [0,9] How do I find A?

This is not a well-posed question, at least for my feeble brain.

Quote:
 Given that $(A^T)^{-1} = \begin{bmatrix} 2 &7 \\ 0 & 9 \end{bmatrix}$, how do I find A ?
Then you are saying that the inverse of the transpose is given.

Well the inverse of the transpose is the transpose of the inverse, so...

$(A^T)^{-1} = (A^{-1})^T = \begin{bmatrix}
2 &7 \\
0 & 9
\end{bmatrix}$
, so transposing gives...

$A^{-1} = \begin{bmatrix}
2 &0 \\
7 & 9
\end{bmatrix}$

The inverse of this 2x2 matrix is A. Find it!

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