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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 $k_1,\cdots,k_4$?

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