Take s and t such that . Let be such that . Now, what can you say about ?
If a matrix equation has two solutions then why does it have infinitely many solutions?
Clue: if and are solutions then look into
Now, I really don´t know where to start on this one. I would appreciate some help just to get started.
This line
means that represents the multitude of solutions.Right?
And if i rewrite the original equation to and prove that it´s true for any then im done. Right?
I tried this:
Now I can do that right? Because and are scalars.
And since
I get
I can rewrite the equation to
because
The final equation looks like this
which is true for any since is a scalar and can be divided from the equation.
Honestly, if this is correct I´m still unsure so any enlightment is still appreciated.
I´m not quite sure if I understand. I see that i could cut to the chase a lot faster but I guess it´s the "proof" part that I tried to elaborate from the clue-part. Can I consider your first reply an answer to the problem?
I´m having a hard time grasping the s and t part.
And is there something wrong about my attempt to an answer besides it being unnecessarily long?
I should probably give up since I still do not understand. I´m assuming that and are two different matrixes that satisfy the equation. What´s the purpose of adding them together? Let alone the purpose of adding the for some well chosen values of s and t?
So what can I say about
..nothing really!