Question

Help finding bases for kernel of this matrix

Answer 1

Here is the matrix in question \[\left[\begin{matrix}1 & 3 & 1 &2\\ 1 & 3 & 1 & 4\end{matrix}\right]\]

Answer 2

I got the rref(A) to be \[\left[\begin{matrix}1 & 3 & 1 & 0\\ 0 & 0 & 0 & 1\end{matrix}\right]\]

Answer 3

I'm not quite sure if \[x _{3}\] would be a leading zero or not

Answer 4

I realized it's redundant but not sure where to go from here.

Answer 5

Ok, since \[x_{2}\] and \[x_{3} \] are redundant vectors I found the ker(A) = span\[\left[\begin{matrix}-3 \\ 1 \\ 0 \\ 0 \end{matrix}\right]\] ,\[\left[\begin{matrix}-1 \\ 0 \\ 1 \\ 0 \end{matrix}\right]\]