Can you please help me solve question 1 and 3? In Exercises 1–4, each of the linear systems has one eigenvalue and one line of eigenvectors. For each system:(a) Find the eigenvalue.(b) Find an eigenvector.(c) Sketch the direction field.(d) Sketch the phase portrait, including the solution curve with initial condition \( \mathbf{Y}_0 = (1, 0) \); and(e) Sketch the \( x(t) \)- and \( y(t) \)-graphs of the solution with initial condition \( \mathbf{Y}_0 = (1, 0) \).1. \( \frac{d\mathbf{Y}}{dt} = \begin{pmatrix} -3 & 0 \\ 1 & -3 \end{pmatrix} \mathbf{Y} \)2. \( \frac{d\mathbf{Y}}{dt} = \begin{pmatrix} 2 & 1 \\ -1 & 4 \end{pmatrix} \mathbf{Y} \)3. \( \frac{d\mathbf{Y}}{dt} = \begin{pmatrix} -2 & -1 \\ 1 & -4 \end{pmatrix} \mathbf{Y} \)4. \( \frac{d\mathbf{Y}}{dt} = \begin{pmatrix} 0 & 1 \\ -1 & -2 \end{pmatrix} \mathbf{Y} \)

Name: Can you please help me solve question 1 and 3? In Exercises 1–4, each
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Can you please help me solve question 1 and 3? In Exercises 1–4, each of the linear systems has one eigenvalue and one line of eigenvectors. For each system:(a) Find the eigenvalue.(b) Find an eigenvector.(c) Sketch the direction field.(d) Sketch the