Loser66
  • Loser66
Please, check my stuff: determine the solution set to the system Ax =0 for the given matrix A
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Loser66
  • Loser66
\[\left[\begin{matrix}1-i&2i\\1+i&-2\end{matrix}\right]\] Multiply row 1 by -i , I get \[\left[\begin{matrix}-1-i&2\\1+i&-2\end{matrix}\right]\] add row1+row2.
Loser66
  • Loser66
so, (1+i )x= 2y the solution set will be S= { (1+i)/2 t, t| t in R} but it's wrong. I don't know why??
anonymous
  • anonymous
\[\left[\begin{matrix}1-i & 2i \\ 1+i & 2\end{matrix}\right]\left(\begin{matrix}a \\ b\end{matrix}\right)=\left(\begin{matrix}0 \\ 0\end{matrix}\right)\] multiply out and solve for a & b

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anonymous
  • anonymous
(1-i)(-i)=-i +i^2 = -1-i
anonymous
  • anonymous
check if det[A] = 0 because if it's not 0 then the 0 vector is only solution.
Loser66
  • Loser66
so, what 's wrong with mine?
Loser66
  • Loser66
nope, it's not that, friend.
anonymous
  • anonymous
? it's not what?
anonymous
  • anonymous
yeah, det[A] = 0 so there's a non-trivial solution.
Loser66
  • Loser66
since the matrix has one 0 row, therefore, there is one free variable, the solution set is infinite set . the result from book said that it is S ={ (1-i)t,t|t is in R}, not as what I did
anonymous
  • anonymous
take a row... (1+i)x = 2y solve for y. y = (1+i)/2 * x
anonymous
  • anonymous
let x = t, then y = [(1+i)/2]t
Loser66
  • Loser66
the same with mine, but it's not right. so. that's why I want you check what's wrong.
anonymous
  • anonymous
it should be the same thing... to check, just solve for x in terms of y... y=(1+i)/2 * x => (1+i)x=2y => x = 2y/(1+i) now to divide mult by conjugate... \[ x=\frac{2y\cdot(1-i)}{1+1}=(1-i)y\] now let t = y then x = (1-i)t
anonymous
  • anonymous
make sense?
Loser66
  • Loser66
give me time to read, does my requirement make sense?
anonymous
  • anonymous
yur requirement? not following
Loser66
  • Loser66
just joke. you just post and then asked me "make sense?" so I required time to read. hihihi
anonymous
  • anonymous
yeah, sorry... please take your time and let me know.
Loser66
  • Loser66
ok, it makes sense to me now. thank you.
anonymous
  • anonymous
you're welcome... i forget that i've already worked it out and of course it makes sense to me and then I forget you've not had the time to look and digest. sorry!
Loser66
  • Loser66
hehehe... that's my fault. thanks again
anonymous
  • anonymous
no... it's mine!

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