Each coefficient matrix A in Problems 25 through 30 is th sum of a nilpotent matrix and a multiple of the identity matrix Use this fact (as in Example 6) to solve the given initial valu problem. 25. x' х 3 2 5 х, x(0) 7

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Q: 1. Find the numerical rank with tolerance 0.9 of the matrix 3 2 A = -4 -5

A: Answer

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A: see the handwritten solution

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A: This is a problem of Vector Space.

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Q: The Attached coefficient matrix A in Problem is the sum of a nilpotent matrix and a multiple of the…

A: Given x'=30006300963012963x,x(0)=1111

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Q: 2. Find the general solution of the system of differential equations d 8 -5 х. dt 10 6 Hint: The…

A: The solution is given as follows

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Q: 16 - х For what value of x, 13. 47 is a singular matrix: - A. 1 В. 2 С. -1 D. -2 E. None of the…

A: A matrix A is said to be singular if its determinant is zero .

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Q: 1. Compute the solution to the following initial value problem y' + y = x, y(0) = 1 Using Picard…

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Q: The Attached coefficient matrix A in Problem is the sum of a nilpotent matrix and a multiple of the…

A: we have been given the matrix  x'=500105020305x, x(0)=405060