1. ## NullSpace

Let S be the subspace of R4 given by the solution set of the equations
-x3 + 4 x4 = -x2 - x3 + x4 and -x1 - x3 = -x1 - 3 x3 = x2

An example of a matrix for which S is the nullspace is....

i tried doing 1 1 0 0
0 1 0 3

2. Originally Posted by ah-bee
Let S be the subspace of R4 given by the solution set of the equations
-x3 + 4 x4 = -x2 - x3 + x4 and -x1 - x3 = -x1 - 3 x3 = x2

An example of a matrix for which S is the nullspace is....

i tried doing 1 1 0 0
0 1 0 3
$-x_3 + 4 x_4 = -x_2 - x_3 + x_4 \Rightarrow x_2 = -3 x_4$ .... (1)

$-x_1 - x_3 = -x_1 - 3 x_3 \Rightarrow x_3 = 0$ .... (2)

$-x_1 - x_3 = x_2 \Rightarrow x_1 = -x_3 - x_2$ .... (3)
Substitute from (1) and (2): $x_1 = 3 x_4$.

So elements of S have the form $x_4 (3, -3, 0, 1)$.

So the example you propose works.

3. the problem is.. when i enter my solution into the web page (online assignment), it says that it is wrong. any ideas why?

4. Originally Posted by ah-bee
the problem is.. when i enter my solution into the web page (online assignment), it says that it is wrong. any ideas why?
1. Perhaps a 4x4 matrix is wanted ....? In which case the question should be more specific on the dimension required.

2. Have you correctly copied the system of equations?

5. 1. I gave a 2x4 matrix in a similar practice question and got it right + there are no specific matrix dimensions required.

2. Yeah, I've copied the equations down correctly.