Chapter 8. Linear Algebra : Matrix Eigenvalue Problems
1
8.1 Eigenvalues, Eigenvectors
Denition Eigenvalues, Eigenvectors
Let A = [ajk ] be an n n matrix. Consider
Ax = x.
(1)
Clearly, x = 0 is a solution of (1). When (1) has a nonzero solution x = 0,
is
Chapter 7. Linear Algebra: Determinants. Linear Systems
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7.3 Linear Systems of Equations. Gauss Elimination
[Linear systems, coecient matrix, augmented matrix]
a11x1 + + a1nxn = b1
a21x1 + + a2nxn = b2
am1x1 + + amnxn = bm
(1)
linear system of m equation
Chapter 4. Systems of ODEs. Phase Plane
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4.1 Systems of ODEs as Models
Example 1. (Mixing Problem Involving Two Tanks)
Initially, tank T1: 100 gal of pure water,
tank T2: 100 gal of water dissolved 150 lb of fertilizer.
By circulating liquid at a rate of