Consider the linear system y→′ = [−3 −2 5 3]y→. a. Find the eigenvalue

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Consider the linear system y→′ = [−3 −2 5 3]y→. a. Find the eigenvalues and eigenvectors for the coefficient matrix. λ1 = , v→1 = [ ], and λ2 = , v→2 = [ ] b. Find the real-valued solution to the initial value problem {y1′ = −3y1 − 2y2, y1(0) = −2 y2′ = 5y1 + 3y2, y2(0) = 5 Use t as the independent variable in your answers. y1(t) = y2(t) =

Consider the linear system y→′ = [−3 −2 5 3]y→. a. Find the eigenvalues and eigenvectors for the coefficient matrix. λ1 = , v→1 = [ ], and λ2 = , v→2 = [ ] b. Find the real-valued solution to the initial value problem {y1′ = −3y1 − 2y2, y1(0) = −2 y2′ = 5y1 + 3y2, y2(0) = 5 Use t as the independent variable in your answers. y1(t) = y2(t) =

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Consider the linear system

{\vec{y}}^{'} = [\begin{array}{rr} - 3 & - 2 \\ 5 & 3 \end{array}] \vec{y} .

a. Find the eigenvalues and eigenvectors for the coefficient matrix.

λ_{1} = ◻, {\vec{v}}_{1} = [\begin{matrix} ◻ \\ ◻ \end{matrix}], and λ_{2} = ◻, {\vec{v}}_{2} = [\begin{array}{l} ◻ \\ ◻ \end{array}]

b. Find the real-valued solution to the initial value problem

{\begin{cases} y_{1}^{'} = - 3 y_{1} - 2 y_{2}, & y_{1} (0) = - 2 \\ y_{2}^{'} = 5 y_{1} + 3 y_{2}, & y_{2} (0) = 5 \end{cases}

Use

t

as the independent variable in your answers.

\begin{array}{l} y_{1} (t) = ◻ \\ y_{2} (t) = ◻ \end{array}

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