1. ## null space

I have attached the question. Am not sure how to work this, out expect by guessing?

2 0
0 3 multiply that by 3,-2 = 0 ,

is this correct ? or is there 'proper way of working this out ?

2. ## Re: null space

We want:

$\begin{bmatrix}a&b\\c&d \end{bmatrix} \begin{bmatrix}3\\-2 \end{bmatrix} = \begin{bmatrix}0\\0 \end{bmatrix}$

but also:

since the null space is spanned by a single vector, nullity(A) = 1.

Now, nullity(A) + rank(A) = 2, therefore: rank(A) = 1.

So let's make A into a rank 1 matrix the easiest way possible, by setting c = d = 0.

This gives us the single equation:

3a - 2b = 0.

If we pick any value we like for b, a is completely determined as a = 2b/3.

To avoid fractional values, let's pick b = 3. What matrix do we get?

By the way, there is more than one correct way to do this, there are MANY possible matrices that would work.