Find a Basis for the Null Space of the Matrix $$A = \left[ \begin{array} { r r r r r } 1 & 0 & - 4 & 0 & - 4 \\0 & 1 & 2 & 0 & 2 \\0 & 0 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

question 68

Multiple Choice

Find a basis for the null space of the matrix.
- $$A = \left[ \begin{array} { r r r r r } 1 & 0 & - 4 & 0 & - 4 \\0 & 1 & 2 & 0 & 2 \\0 & 0 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

• A)
• \( \left\{\left[\begin{array}{r}-4 \\ 2 \\ 1 \\ 0 \\ 0\end{array}\right],\left[\begin{array}{r}-4 \\ 2 \\ 0 \\ -1 \\ 1\end{array}\right]\right\} \)
• B)
• \[\left\{ \left[ \begin{array} { r }
• - 4 \\
• 2 \\
• 1 \\
• 0 \\
• 0
• \end{array} \right] , \left[ \begin{array} { r }
• - 4 \\
• 2 \\
• 0 \\
• - 1 \\
• 1
• \end{array} \right] \right\}\]
• C)
• \(\left\{\left[\begin{array}{r}
• 1 \\
• 0 \\
• -4 \\
• 0 \\
• -4
• \end{array}\right],\left[\begin{array}{l}
• 0 \\
• 1 \\
• 2 \\
• 0 \\
• 2
• \end{array}\right]\right\}\)
• D)
• \(\left\{\left[\begin{array}{l}
• 1 \\
• 0 \\
• 0 \\
• 0
• \end{array}\right],\left[\begin{array}{l}
• 0 \\
• 1 \\
• 0 \\
• 0
• \end{array}\right],\left[\begin{array}{l}
• 0 \\
• 0 \\
• 1 \\
• 0
• \end{array}\right]\right\}\)

---

Definitions:

Planning Function

An essential management activity that involves setting objectives and determining a course of action for achieving those objectives.

Nonprogrammed Decision

This type of decision is made in response to situations that are unique, are poorly defined and largely unstructured, and have important consequences for the organization.

Reordering

The process of ordering additional stock to replenish inventory before it runs out.