Let A be a square matrix defined by 2 -1 -2 A = 4 -3 -2...

 

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Let A be a square matrix defined by 2 -1 -2 A = 4 -3 -2 %3D 5 -1 -5 (a) Find the eigenvalues and eigenspaces of A. (b) Show that A is diagonalizable. Diagonalize A. dx (c) Solve the system of linear differential equations dt Ax where = (x1, 12, T3)". %3D dx Then solve the initial value problem Ax + B (t), x (0) = (0,0, 1)" where B (t) = dt (e", 3e“, –5eª)". Let A be a square matrix defined by 2 -1 -2 A = 4 -3 -2 %3D 5 -1 -5 (a) Find the eigenvalues and eigenspaces of A. (b) Show that A is diagonalizable. Diagonalize A. dx (c) Solve the system of linear differential equations dt Ax where = (x1, 12, T3)". %3D dx Then solve the initial value problem Ax + B (t), x (0) = (0,0, 1)" where B (t) = dt (e", 3e“, –5eª)".

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FOR THE GIVEN MATRIX A AI0 2 1 2 4 3 2 5 1 5 0 23521 14... View the full answer