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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