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Q.1 Suppose that A is a 3 x 3 matrix with eigenvalues A =-1, A2 = 0 and A3 1, and corresponding eigenvectors () i2 = Üz = 2. a) Find the matrix A. b) Compute the matrix A20.

Q.1 Suppose that A is a 3 x 3 matrix with eigenvalues A =-1, A2 = 0 and A3 1, and corresponding eigenvectors () i2 = Üz = 2. a) Find the matrix A. b) Compute the matrix A20.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q.1 Suppose that A is a 3 x 3 matrix with eigenvalues A1 = -1, A2 = 0 and 3 = 1, and corresponding eigenvectors %3D () U3 = 2. a) Find the matrix A. b) Compute the matrix A20. Q.2 Diagonalize A if possible. Also find Eigen values of A + 41 & A¯³ , where 7 1 -2 A = -3 6. 2 2 Q.3 Solve the system of differential equations dr =2x + y dt dy =r+2y for the unknown functions r(t) and y(t), subject to the initial conditions r(0) = 1 and y(0) = 5. 3.
Transcribed Image Text:Q.1 Suppose that A is a 3 x 3 matrix with eigenvalues A1 = -1, A2 = 0 and 3 = 1, and corresponding eigenvectors %3D () U3 = 2. a) Find the matrix A. b) Compute the matrix A20. Q.2 Diagonalize A if possible. Also find Eigen values of A + 41 & A¯³ , where 7 1 -2 A = -3 6. 2 2 Q.3 Solve the system of differential equations dr =2x + y dt dy =r+2y for the unknown functions r(t) and y(t), subject to the initial conditions r(0) = 1 and y(0) = 5. 3.
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