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(a) For each of the matrices A below find a general solution to the system x'(t) = Ax(t) 3/4` 3 (-1 ³/4) 4- (121) -5 3 (i) A = (ii) A= (b) Solve each of the initial value problems below 1 3 -3 (i) x'(t) = (², ³) x(t), x(0) = = (³)_ (ii) x'(t) = (2 −7³) x(t), x(0) = (-10) 3 1

(a) For each of the matrices A below find a general solution to the system x'(t) = Ax(t) 3/4` 3 (-1 ³/4) 4- (121) -5 3 (i) A = (ii) A= (b) Solve each of the initial value problems below 1 3 -3 (i) x'(t) = (², ³) x(t), x(0) = = (³)_ (ii) x'(t) = (2 −7³) x(t), x(0) = (-10) 3 1

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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(a) For each of the matrices A below find a general solution to the system x'(t) = Ax(t) 3 = (= 1 ³/4) (ii) A = 4- (121) 3 (i) A (b) Solve each of the initial value problems below 1 -3 (i) x'(t) = (² i) x(t), x(0) = = (³)_ (ii) x'(t) = (2 −7³) x(t), x(0) = (-10) 3
Transcribed Image Text:(a) For each of the matrices A below find a general solution to the system x'(t) = Ax(t) 3 = (= 1 ³/4) (ii) A = 4- (121) 3 (i) A (b) Solve each of the initial value problems below 1 -3 (i) x'(t) = (² i) x(t), x(0) = = (³)_ (ii) x'(t) = (2 −7³) x(t), x(0) = (-10) 3
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