Chapter 4 - Vector Spaces - 4.3 Subspaces - Problems - Page 273: 23

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Given $A=\begin{bmatrix} 1 & 4 \end{bmatrix}$ Since $x,y \in nullspace (A)$ we obtain $Ax=0\\ \begin{bmatrix} 1 & 4 \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix}=0\\ x+4y=0\\ x=-4y$ Hence, nullspace $(A) =\{(x,y)\in R^2:x=-4y\}$