Question

For each matrix$\mathit{A}$in exercises 1 through 13, find vectors that span the kernel of $\mathit{A}$. Use paper and pencil.

3.$\mathit{A}\mathbf{=}\mathbf{\left[}\begin{array}{cc}\mathbf{0}& \mathbf{0}\\ \mathbf{0}& \mathbf{0}\end{array}\mathbf{\right]}$

Short answer

The kernel of$A$is $ker\left(A\right)=span\left({\stackrel{I}{e}}_1,{\stackrel{I}{e}}_2\right)$.

Step-by-step solution

The kernel of a matrix

The kernel of a matrix$\mathit{A}$is the solution set of the linear system$\mathit{A}\overrightarrow{\mathbf{x}}\mathbf{=}\mathbf{0}$.

Find kernel of the given matrix

Here, the given matrix is in reduced row-echelon form. Notice that the given matrix is a zero matrix. So, the solution set of $A\overrightarrow{x}=0$are all vectors $\overrightarrow{x}$lies in.${ℝ}^2$

Thus,$\ker \left(A\right)=span({\overrightarrow{e}}_1,{\overrightarrow{e}}_2)$ .