The 2 × 2 matrix A has a repeated eigenvalue 3. Moreover, we have (A – 31)v= w and (A – 31)w = 0 where v = (1,0)T, w = (1, –1)". %3D %3m

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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[Differential Calculus] How do you solve this?

The 2 x 2 matrix A has a repeated eigenvalue 3. Moreover, we have (A – 31)v= w and (A – 31)w = 0 where
v = (1,0)", w = (1, –1)".
(a) Write out the general solution of the equation æ' = Ax.
(b) Find eAt.
(c) Find a solution of the equation x' = Ax with initial condition x(0) = (2,3)².
Transcribed Image Text:The 2 x 2 matrix A has a repeated eigenvalue 3. Moreover, we have (A – 31)v= w and (A – 31)w = 0 where v = (1,0)", w = (1, –1)". (a) Write out the general solution of the equation æ' = Ax. (b) Find eAt. (c) Find a solution of the equation x' = Ax with initial condition x(0) = (2,3)².
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