Calculate[ri(t) r₂(t)] and[r(t) x r₂(t)] first by differentiating the product directly and then by applying the formulas d dr₂ dr (t)-r₂(t)]=r₁(t)- + -r₂(t) and dt dt dr₂ dr₁ d[r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt ri(t) = 6ti + 4t²j+ 4t³k, r₂(t) = t¹k r(t)-r₂(t)] = [ r(t) r₂(t)]=

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Calculate[ri(t) r2(t)] and [r₁(t) x r2(t)] first by differentiating
the product directly and then by applying the formulas
[r₁(t)- r₂(t)]=r₁(t). +
dr₂ dr
dt dt
r₂(t) and
dr₂, dr
[r(t) x r₂(t)]=r(t) x +
x r₂(t).
dt dt
r₁(t) = 6ti + 4t²j + 4t³k, r₂(t) = t¹k
[r₁(t)- r₂(t)] = [
[r₁(t) × r₂(t)] = [
dt
Transcribed Image Text:Calculate[ri(t) r2(t)] and [r₁(t) x r2(t)] first by differentiating the product directly and then by applying the formulas [r₁(t)- r₂(t)]=r₁(t). + dr₂ dr dt dt r₂(t) and dr₂, dr [r(t) x r₂(t)]=r(t) x + x r₂(t). dt dt r₁(t) = 6ti + 4t²j + 4t³k, r₂(t) = t¹k [r₁(t)- r₂(t)] = [ [r₁(t) × r₂(t)] = [ dt
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