If o is a normalised fundamental matrix of X = AX at to = 0 and f is continuous in t, then Xp(t) = | (t – s)F(8) ds is a particular solution of X = AX +F. Use the above result to find a general solution of 2 X + -1 3

Q: 2. Regarding DFT matrix W₁, prove that W 1 = W for N=4. N

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A: Given: A=210020012

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A: Topic = Functions

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A: We will solve the matrix operation.

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A: Singular Matrix

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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A: To solve the initial value problem

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A: I am attaching image so that you understand each and every step.

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Q: e singular values

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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.