We deduce that .
We choose and . Then . This is the third column of which is . Finally, .
Let's check independence of the columns and invertibility of the matrix right now.
, so is invertible. This also tells us that the row space (and thus the column space) has dimension 4. It follows that the columns are independent.
Now we check that .
It doesn't work can someone tell me why?
It seems that the only vector working is !