(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Linear Algebra: given adj(A) find A

1. The problem statement, all variables and given/known data

If [tex]adj\mathbb A = \left(\begin{array}{ccc}1&0&1\\1&-1&0\\0&2&1\end{array}\right)[/tex], findA. Briefly justify your algorithm.

2. Relevant equations

[tex]adj\mathbb A=(det\mathbb A)(\mathbb A^{-1})[/tex]

3. The attempt at a solution

[tex]adj\mathbb A=(det\mathbb A)(\mathbb A^{-1})[/tex]

invert both sides to get:

[tex](adj\mathbb A)^{-1} = [(det\mathbb A)(\mathbb A^{-1})]^{-1}[/tex]

[tex](adj\mathbb A)^{-1} = (\mathbb A^{-1})^{-1}(det\mathbb A)^{-1}[/tex]

[tex](adj\mathbb A)^{-1} = (\mathbb A)(\frac{1}{det\mathbb A})[/tex]

[tex]\mathbb A = (det\mathbb A)(adj\mathbb A)^{-1}[/tex]

My, isn't that nice.

I computed [tex](adj\mathbb A)^{-1}[/tex], and found it to be

[tex]\left(\begin{array}{ccc}-1&2&1\\-1&1&1\\2&-2&-1\end{array}\right)[/tex]

But I have no clue how to find detA, so I'm stuck with one equation:

[tex]\mathbb A = (det\mathbb A)(adj\mathbb A)^{-1}[/tex]

and two unknowns:

[tex]\mathbb A[/tex] and [tex]det\mathbb A[/tex]

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# Homework Help: Linear Algebra: given adj(A) find A

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