# Kernel Matrix Calculation

Question:

Calculate the Kernel of:

$$F(x) = Ax$$

$$A=\begin{pmatrix}1 &-2& 4& 0\\ -3& -4& 10& -1\\ 5 & 0& -2& 1\\ 6 &-2 & 2& 1\end{pmatrix}$$

I know that the Kernel is the Matrix with which the Gauss-Algorithm of $$A$$ should have the value $$0$$. But when I calculate the Matrix with the Gauss-Algorithm I come to the result of:

$$\begin{pmatrix}1& -2& 4& 0\\ 0 &-10 &-22 &0\end{pmatrix}$$

But what is my Kernel now? I mean do I not need all the 4 values $$k_1,\cdots,k_4$$?