For the Given Matrix A, Find a Basis for the Corresponding

question 19

Multiple Choice

For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue.
- $A = \left[ \begin{array} { r r r } - 4 & 0 & 0 \\ - 10 & 6 & 0 \\ - 30 & 16 & - 2 \end{array} \right] , \lambda = - 4$

• A)
• \(\left\{ \left[ \begin{array} { r } 1 \\ - 1 \\ - 7 \end{array} \right] \right\}\)
• B)
• \(\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 0 \\ - 7 \end{array} \right] \right\}\)
• C)
• \(\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 7 \end{array} \right] \right\}\)
• D)
• \(\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 1 \\ 0 \\ 7 \end{array} \right] \right\}\)

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Definitions:

Net Income

The amount of money left over after all expenses and taxes have been subtracted from total revenue.

Units

Units refer to the individual components or quantities of a product, investment, or other items that are counted or measured.

Month

A unit of time, roughly based on the period of the Moon's orbit around Earth, traditionally used to measure durations of approximately 30 days.

Break Even

The point at which total costs and total revenue are equal, resulting in no net loss or gain.