I have the matrix
1st line [1 0 1 -2]
2nd line [1 1 -3 4]
3rd line [3 1 -1 0]
4th line [4 2 -4 4]
5th line [0 1 -4 6]
I need to transform it from R5 to R4, ann then find the base nullity. How do I go about doing this and if possible show a working out. Cheers
The matrix you end up with is actually:
Now if you done the row-reductions (assuming you were correct!) we get:
You can bring the bottom three rows to:
However this matrix is still now in row-reduced echelon form.
We will add the (3rd row 2) to 2nd row and 1st row.
Finally, add (2nd row ) to 1st row:
This tells you that:
Thus, (notice that is "free").
This means if then solves , and conversely.
Thus, the nullspace is
We see the dimension is one, and so the nullity is one.