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chrisplusian
 one year ago
Linear algebra question.... see attachment please
chrisplusian
 one year ago
Linear algebra question.... see attachment please

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chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0Can you see the attachment?

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1Yes it is possible.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let's call the matrix on the RHS \(M\), so you have \[{\bf{AB}}={\bf{M}}\] If \({\bf{A}}\neq0\), you can find its inverse \({\bf{A}}^{1}\), which is pretty straightforward since it's 2x2. Then \[{\bf{B}}={\bf{A}}^{1}{\bf{M}}\] Then you can find the inverse of \(\bf{B}\), provided it's not singular.

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1Both \(\bf{AB}\) and \(\bf{A}\) have full rank.

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0^^^ that was my attempt but it did not work out

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1\[ \det(\mathbf{A})=5(3)(3)=59=4\neq5+9=13 \]

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0I see that now!!! is my approach correct?

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1\[ \mathbf{A}^{1}\text{ and }\mathbf{AB}^{1}\text{ exist.}\\ \mathbf{A}^{1}\mathbf{AB}=\mathbf{B}\\ \mathbf{B}^{1}=\left(\mathbf{A}^{1}\mathbf{AB}\right)^{1}=\left(\mathbf{AB}\right)^{1}\mathbf{A}\\ \left(\left(\mathbf{AB}\right)^{1}\mathbf{A}\right)\mathbf{B}=\left(\mathbf{AB}\right)^{1}\left(\mathbf{A}\mathbf{B}\right)=\mathbf{I}\\ \mathbf{B}\left(\left(\mathbf{AB}\right)^{1}\mathbf{A}\right)=\mathbf{A}^{1}\mathbf{AB}\left(\left(\mathbf{AB}\right)^{1}\mathbf{A}\right)=\mathbf{A}^{1}\left(\mathbf{AB}\left(\mathbf{AB}\right)^{1}\right)\mathbf{A}=\mathbf{I}\\ \therefore \mathbf{B}^{1}=\left(\mathbf{AB}\right)^{1}\mathbf{A} \]

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0^^^ I wish I could see it that way.

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0If I could give you another medal for that answer I would lol
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