.

We deduce that .

We choose and . Then . This is the third column of which is . Finally, .

Let .

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 !