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DLSBest ResponseYou've already chosen the best response.1
\[If~A=\left[\begin{matrix}\alpha & 0 \\ 1 & 1\end{matrix}\right] \] \[\And~B=\left[\begin{matrix}1 & 5 \\ 0 & 1\end{matrix}\right]\] such that \[A^2=B\] Then \[\alpha=?\]
 one year ago

DLSBest ResponseYou've already chosen the best response.1
Options: A)1 B)1 C)4 D)None of these
 one year ago

DLSBest ResponseYou've already chosen the best response.1
\[\LARGE \left[\begin{matrix}\alpha^2 & 0 \\ \alpha+1& 1\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 5 & 1\end{matrix}\right]\] I am getting this after equating A^2=B I am getting all the 3 options A,B,C. But it is a single choice question.
 one year ago

DLSBest ResponseYou've already chosen the best response.1
@agent0smith @dmezzullo @electrokid
 one year ago

phiBest ResponseYou've already chosen the best response.1
the lower left entry should be in B is 0. so you have a^2 =1 and a+1=0
 one year ago

phiBest ResponseYou've already chosen the best response.1
are you sure about the B matrix? A*A is [ a^2 0 ] [ a+1 1 ] which cannot match B as given
 one year ago

phiBest ResponseYou've already chosen the best response.1
which version of B is the one given? the original or the one you posted later?
 one year ago

agent0smithBest ResponseYou've already chosen the best response.0
\[~B=\left[\begin{matrix}1 & 5 \\ 0 & 1\end{matrix}\right] \] \[\LARGE \left[\begin{matrix}\alpha^2 & 0 \\ \alpha+1& 1\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 5 & 1\end{matrix}\right]\] which is B...
 one year ago

agent0smithBest ResponseYou've already chosen the best response.0
so alpha^2 = 1 and alpha+1 = 5...??? that doesn't seem to work :/
 one year ago

phiBest ResponseYou've already chosen the best response.1
as you noticed, there is no unique solution for alpha...
 one year ago

DLSBest ResponseYou've already chosen the best response.1
A,B,C all 3 are correct but single choice ..
 one year ago

agent0smithBest ResponseYou've already chosen the best response.0
If you're sure that second matrix is right, then there's no solution. The first matrix would give alpha is 1.
 one year ago

phiBest ResponseYou've already chosen the best response.1
I think you should choose option D
 one year ago

DLSBest ResponseYou've already chosen the best response.1
yes it is right : the solution says none of these since this is an absurd case :O
 one year ago
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