solve for a,b,c,d
a^2 + bc + 2a +3 =0
b(a+d) +2b =0
c(a+d) +2c = 0
cb +d^2 +2d + 3 =0
Please

Question

solve for a,b,c,d
a^2 + bc + 2a +3 =0
b(a+d) +2b =0
c(a+d) +2c = 0
cb +d^2 +2d + 3 =0 
Please

loser66 · Answer

@tkhunny  it comes from the previous post. I have no way to solve. Try this way :( if you have any idea, please, teach me

tkhunny · Answer

Shall we first rule out the trivial solutions?  b = c = 0, for example?

loser66 · Answer

no, I need ad - bc $\neq 0$ to have A invertible. Cannot use that posibility

tkhunny · Answer

b = c= 0 does not violate that, as long as "ad" is not zero.

loser66 · Answer

yes, got it.

loser66 · Answer

@eashy I have no way to solve it. now I try this way. Let me show you
Let A =$\left[\begin {matrix}a&b\c&d\end{matrix}\right]$
then A^2
        2A
         3I
add them together and let it =0 to have a bunch of things on the post.
if A is invertible, ad -bc $\neq 0$ 
and I got it as above. heehe.. done

anonymous · Answer

nice. matrices are very powerful

loser66 · Answer

thanks :)