Question

Matrix help!

Answer 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 \[\alpha=?\]

Answer 2

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

Answer 3

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

Answer 4

@yrelhan4

Answer 5

@agent0smith @dmezzullo @electrokid

Answer 6

the lower left entry should be in B is 0. so you have

a^2 =1
and
a+1=0

Answer 7

no..

Answer 8

are you sure about the B matrix?

A*A is
[ a^2 0 ]
[ a+1 1 ]
which cannot match B as given

Answer 9

yes i checked twice

Answer 10

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

Answer 11

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

which is B...

Answer 12

later one sorry

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

I think you should choose option D

Answer 18

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