Mathematics II20795 marksNumerical: null space verificationNull spaces, Column spaces, and Linear transformations
Define null space of a matrix A. Show that v is in the null space of A, where
Define null space of a matrix $A$. Show that $v$ is in the null space of $A$, where
$$A = \begin{bmatrix} 1 & -3 & -2 \ -5 & 9 & 1 \end{bmatrix}, \qquad v = \begin{bmatrix} 5 \ 3 \ -2 \end{bmatrix}$$
The null space of an $m \times n$ matrix $A$, written $N(A)$ or $\text{Null}(A)$, is the set of all vectors $\mathbf{x}$ in $\mathbb{R}^n$ that satisfy the homogeneous equation $A\mathbf{x} = \mathbf{0}$: $$N(A) = {, \mathbf{x} \in \mathbb{R}^n \mid A\mathbf{x} = \mathbf{0} ,}$$ so the null s...