## DLS Group Title Matrix help! one year ago one year ago

1. DLS Group Title

$If~A=\left[\begin{matrix}\alpha & 0 \\ 1 & 1\end{matrix}\right]$ $\And~B=\left[\begin{matrix}1 & 5 \\ 0 & 1\end{matrix}\right]$ such that $A^2=B$ Then $\alpha=?$

2. DLS Group Title

Options: A)1 B)-1 C)4 D)None of these

3. DLS Group Title

$\LARGE \left[\begin{matrix}\alpha^2 & 0 \\ \alpha+1& 1\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 5 & 1\end{matrix}\right]$ 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.

4. DLS Group Title

@yrelhan4

5. DLS Group Title

@agent0smith @dmezzullo @electrokid

6. phi Group Title

the lower left entry should be in B is 0. so you have a^2 =1 and a+1=0

7. DLS Group Title

no..

8. phi Group Title

are you sure about the B matrix? A*A is [ a^2 0 ] [ a+1 1 ] which cannot match B as given

9. DLS Group Title

yes i checked twice

10. phi Group Title

which version of B is the one given? the original or the one you posted later?

11. agent0smith Group Title

$~B=\left[\begin{matrix}1 & 5 \\ 0 & 1\end{matrix}\right]$ $\LARGE \left[\begin{matrix}\alpha^2 & 0 \\ \alpha+1& 1\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 5 & 1\end{matrix}\right]$ which is B...

12. DLS Group Title

later one sorry

13. agent0smith Group Title

so alpha^2 = 1 and alpha+1 = 5...??? that doesn't seem to work :/

14. phi Group Title

as you noticed, there is no unique solution for alpha...

15. DLS Group Title

A,B,C all 3 are correct but single choice .-.

16. agent0smith Group Title

If you're sure that second matrix is right, then there's no solution. The first matrix would give alpha is -1.

17. phi Group Title

I think you should choose option D

18. DLS Group Title

yes it is right :| the solution says none of these since this is an absurd case :O