[Solved] 18.06 Unit 2 Exercise 10-differential equations and eAt

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Problem 23.1: (6.3 #14.a Introduction to Linear Algebra: Strang) The matrix in this question is skew-symmetric (AT = −A) :

du = −0c 0cba u or uu2 = au3cu13

dt ba 0 u.

Find the derivative of ||u(t)||2 using the definition:

||u(t)||2 = u12 + u22 + u32.

What does this tell you about the rate of change of the length of u? What does this tell you about the range of values of u(t)?

Problem 23.2: (6.3 #24.) Write A as SΛS1. Multiply SeΛtS1

to find the matrix exponential eAt. Check your work by evaluating eAt and the derivative of eAt when t = 0.

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[Solved] 18.06 Unit 2 Exercise 10-differential equations and eAt
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