Find an explicit description of the null space of matrix A by listing vectors that span the null space.
-$$A = \left[ \begin{array} { r r r r }
1 & - 2 & - 2 & - 2 \
0 & 1 & 3 & 4
\end{array} \right]$$
A)
$\left[ \begin{array} { r } - 4 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } - 6 \ - 4 \ 0 \ 1 \end{array} \right]$

B)
$\left[ \begin{array} { l } 2 \ 1 \ 0 \ 0 \end{array} \right] , \left[ \begin{array} { r } 2 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } 2 \ - 4 \ 0 \ 1 \end{array} \right]$

C)
$\left[ \begin{array} { l } 2 \ 1 \ 0 \ 0 \end{array} \right] , \left[ \begin{array} { r } - 4 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } - 6 \ - 4 \ 0 \ 1 \end{array} \right]$

D)

$\left[ \begin{array} { r } 2 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } 2 \ - 4 \ 0 \ 1 \end{array} \right]$

Question

Find an explicit description of the null space of matrix A by listing vectors that span the null space.
-$$A = \left[ \begin{array} { r r r r } 
1 & - 2 & - 2 & - 2 \
0 & 1 & 3 & 4
\end{array} \right]$$
A)
$\left[ \begin{array} { r } - 4 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } - 6 \ - 4 \ 0 \ 1 \end{array} \right]$

B)
$\left[ \begin{array} { l } 2 \ 1 \ 0 \ 0 \end{array} \right] , \left[ \begin{array} { r } 2 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } 2 \ - 4 \ 0 \ 1 \end{array} \right]$

C)
$\left[ \begin{array} { l } 2 \ 1 \ 0 \ 0 \end{array} \right] , \left[ \begin{array} { r } - 4 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } - 6 \ - 4 \ 0 \ 1 \end{array} \right]$

D)

$\left[ \begin{array} { r } 2 \ - 3 \ 1 \ 0 \end{array} \right] , \left[ \begin{array} { r } 2 \ - 4 \ 0 \ 1 \end{array} \right]$

Quizplus · Accepted Answer

The null space of a matrix consists of all vectors that satisfy $A\mathbf{x} = \mathbf{0}$. For the given matrix, solving the system of equations represented by $A\mathbf{x} = \mathbf{0}$ leads to the vectors in choice A, which correctly span the null space.

Find an Explicit Description of the Null Space of Matrix A=[1−2−2−20134]A = \left[ \begin{array} { r r r r } 1 & - 2 & - 2 & - 2 \\0 & 1 & 3 & 4\end{array} \right]A=[10​−21​−23​−24​]

Find an Explicit Description of the Null Space of Matrix $A = \left[ \begin{array} { r r r r } 1 & - 2 & - 2 & - 2 \\0 & 1 & 3 & 4\end{array} \right]$