The eigenvalues of the coefficient matrix A are given. Find a general solution of the indicated system x′=Ax.   x′=   75 16 −32   −72 −13 32 144 32 −61x​;    λ=−5​, 3​, 3       x(t)=enter your response here

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A: Given:To Solve: , where .

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Q: [3 1 -1] 21 0 li 5 -1.

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Q: determine the general solution to the linear system x′= Ax for the given matrix A.

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A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

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A: Given the equations are y1 - y3 = 12y1 + 3y2 - y3 = 1y1 - y2 - y3 = 3

Q: Use the following matrices to perform the operation, if possible. (If not possible, enter IMPOSSIBLE…

A: C=9101D=2653

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A: To find the value of x2 using the given augmented matrix.

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Q: a. Solve the following system of linear equations by Gauss Jordan method x +y = 3 3x + 2y = 7

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Q: Find the cofactor matrix of the following matrix 1 0 1 A = 4 -2 5 1

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Q: 0 1 1 1 0 3 and B = 100 1 20 0 (a) Solve the following equation for X: BAXA - B (b) You should have…

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Q: Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 14 1 4…

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Q: Consider the set L:= {(a,b) E Z²| (a – b) is a multiple of 3}. A proposed recursive definition for L…

A: Consider the provided question. L=a,b∈L'a-b is multiple of 3 therefore, a-b=3ka=b+3k  where k is an…

Q: (4) Given matrix A = ( ), and that h(T) = T² – 2T – 7, find h(T).

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Q: 5. Use the matrices to solve the x-2y+3z = 4 system: 3x- 4y+z = 4 2x +3y-4z = -2

A: We have to solve the equation by matrix method.

Q: Let A be the matrix 4 2 7 6 Find p(A). p(x) = x – 2x + 4 i i p(A) =

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