Use the definition of the matrix exponential to compute eA for each of the following matrices: A=begin{bmatrix}1 & 0&-1 0 & 1&00&0&1 end{bmatrix}

Haven 2020-12-28 Answered
Use the definition of the matrix exponential to compute eA for each of the following matrices:
A=[101010001]
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Expert Answer

Theodore Schwartz
Answered 2020-12-29 Author has 99 answers
Step 1
Given matrix is
A=[101010001]
Step 2 Now A2=AA
=[101010001][101010001]
=[102010001]
A3=A2A
=[102010001][101010001](using values of A2 and A)
=[103010001]

In general
An=[10n010001] for n1
Step 3
Now by the definition of the matrix exponential
eA=I+A+A22!+A33!+
=[101010001]+[101010001]+12![102010001]+13![103010001]+
=[1+1+12!+13!+00(1+1+12!+12!+)01+1+12!+12!+0001+1+12!+12!+]
=[e0e0e000e]
Step 4
Answer:
eA=[e0e0e000e]
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Jeffrey Jordon
Answered 2022-01-27 Author has 2047 answers

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