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 ?
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.