V. Consider the homogeneous first-order linear differential system yi = 2yı + 2y2 + 2y3 y, = 3y2 + Y3 Y3 = y2 + 3y3 where y,'s are all functions of the variable z. i. Write the system in the matrix form Y' = AY and determine the matrix A. ii. Is the matrix A diagonalizable? Explain.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.