MAS 801 It's a Discreetly Discrete World – Mathematics in ... - Spms
MAS 801 It's a Discreetly Discrete World – Mathematics in ... - Spms
MAS 801 It's a Discreetly Discrete World – Mathematics in ... - Spms
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Example<br />
• F<strong>in</strong>d all the eigenvectors of A =<br />
3 1<br />
1 3<br />
• We know the eigenvalues are 2 and 4<br />
• Let’s first try to f<strong>in</strong>d the eigenvectors correspond<strong>in</strong>g to eigenvalue 2<br />
• We have to f<strong>in</strong>d x such that Ax = 2x<br />
3 1<br />
1 3<br />
x1<br />
x2<br />
=<br />
2x1<br />
2x2<br />
<br />
3x1 + x2<br />
x1 + 3x2<br />
=<br />
2x1<br />
2x2<br />
• We get x1 + x2 = 0; if we let x1 = k then x2 = -k<br />
• The eigenvectors are given by k , where k ≠ 0<br />
-k
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