Unformatted text preview: 1,1},{1,3,2},{1,2,4}}; Eigenvalues[a]
The answer is so complicated because Mathematica uses exact but complicated
formulae for solving cubics discovered by Cardan and Tartaglia, two sixteenth
century Italian mathematicians.
b. Find numerical approximations to these eigenvalues by running the program
Eigenvalues[N[a]]
The numerical values of the eigenvalues are far easier to use.
c. Use Mathematica to ﬁnd numerical values for the eigenvectors for A by
running the Mathematica program
Eigenvectors[N[a]]
and write down the general solution to the matrix diﬀerential equation
dx
= Ax.
dt
48 1 Figure 2.5: Two carts connected by springs and moving along a frictionfree
track. 2.4 Mechanical systems Mechanical systems consisting of weights and springs connected together in an
array often lead to initial value problems of the type
d2 x
= Ax,
dt2 x(0) = f , dx
= 0,
dt (2.13) where A is a symmetric matrix and f is a constant vector. These can be solved
by a technique similar to that used in th...
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 Winter '14
 Equations

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