Categorize the eigenvalues and eigenvectors of the coefficient matrix A according to the accompanying classifications and sketch the phase portrait of the system by hand. Then use a computer system or graphing calculator to check your answer. Click here to view page 1 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes Click here to view page 2 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes Click here to view page 3 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes The system shows a saddle point System of equations Matrix equation '= -2x₁ - 5x2 X₁ x₂ = 4x₁ + 2x2 -2-5 4 Eigenvectors Eigenvalues 21,2 = ± 14 and its eigenvalues are distinct, opposite in sign, and real. x' = V1,2 2 1±i2 -2

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