Maths proof help plsWatch
But for a first step: try to solve (find a matrix that works) for the case where x = (1,0,0,...0); i.e. 1 in the first component, all other components 0.
From there, try to solve for a general x.
Also note that what ever you do has to be valid for , but you are using 2x2 matrices so what you're writing would only be valid in .
Could you give me an idea of how to start it? and then i could try finish it?
You'll then have to work out how if I told you "only the kth component of my vector is non-xero" you could make a similar solution that only divides by x_k.
Also, don't forget that you are going to need to provide a general solution at some point, so you'll need to think about what you'd do for a general n x n matrix and vector .
Wouldn't x2 and x3 always be multiplied by 0 so wouldn't make a difference? I'm stuck with how to turn this to a general solution
How would you change it to only depend on x2?
If you really can't work it out, start from a general 3 x 3 matrix A, and assume x = (0, 1, 0), multiply through, and see what you get, and therefore what you'd need to do to force Ax = y.
So you should now be in a position to write your proof. As a hint, it should probably start with a line something like:
Suppose and x is non-zero. Then we can find k such that . Then...
so do i write three matrices with non-trivial solutions in different columns?
It's perfectly fine to say things like "A is the matrix with all columns zero, except..." however.