The Jacobian Matrix of the System $x ^ { \prime } = x ^ { 3 } - y ^ { 3 } - 8 , y ^ { \prime } = 8 y$

question 30

Multiple Choice

The Jacobian matrix of the system $x ^ { \prime } = x ^ { 3 } - y ^ { 3 } - 8 , y ^ { \prime } = 8 y$ at the critical point $( 2,0 )$

• A) \(A = \left[ \begin{array} { r r }
• 3 x ^ { 2 } & - 3 y ^ { 2 } \\
• 8 & 0
• \end{array} \right]\)
• B) \(A = \left[ \begin{array} { r r }
• 3 x ^ { 2 } & - 3 y ^ { 2 } \\
• 0 & 8
• \end{array} \right]\)
• C) \(A = \left[ \begin{array} { r r }
• 3 x ^ { 2 } & 3 y ^ { 2 } \\
• 0 & 8
• \end{array} \right]\)
• D) \(A = \left[ \begin{array} { c c }
• 12 & 0 \\
• 0 & 8
• \end{array} \right]\)
• E) \(A = \left[ \begin{array} { c c }
• 12 & 0 \\
• 8 & 0
• \end{array} \right]\)

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