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

Question 3

Multiple Choice

For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue.
- A=[400106030162],λ=4A = \left[ \begin{array} { r r r } - 4 & 0 & 0 \\ - 10 & 6 & 0 \\ - 30 & 16 & - 2 \end{array} \right] , \lambda = - 4


A)
{[117]}\left\{ \left[ \begin{array} { r } 1 \\ - 1 \\ - 7 \end{array} \right] \right\}

B)
{[110],[107]}\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 0 \\ - 7 \end{array} \right] \right\}

C)
{[117]}\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 7 \end{array} \right] \right\}

D)

{[110],[107]}\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 1 \\ 0 \\ 7 \end{array} \right] \right\}

Correct Answer:

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