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:

Taxable Income

The amount of an individual's or entity's income used to determine how much tax is owed to the government.

Permitted Deductions

Allowable subtractions from gross income that reduce taxable income, as defined by tax laws.

Flat Tax

A tax system with a constant rate, where taxpayers pay the same percentage of their income regardless of the level of their income.

Marginal Tax Rate

The rate at which the last dollar of income is taxed, indicating the percentage of tax applied to your income for each tax bracket in which you qualify.