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Unformatted text preview: λI2 is zero.10 So we computed
det(C − λI2 ) = det 6−λ
14 35 − λ = (6 − λ)(35 − λ) − 14 · 15 = λ2 − 41λ This is called the characteristic polynomial of the matrix C and it has two zeros: λ = 0
and λ = 41. That’s how we knew to use 41 in our work above. The fact that λ = 0
This material is usually given its own chapter in a Linear Algebra book so clearly we’re not able to tell you
everything you need to know about eigenvalues and eigenvectors. They are a nice application of determinants,
though, so we’re going to give you enough background so that you can start playing around with them.
Think about this. 520 Systems of Equations and Matrices
showed up as one of the zeros of the characteristic polynomial just means that C itself had
determinant zero which we already knew. Those two numbers are called the eigenvalues of
C . The corresponding matrix solutions to CX = λX are called the eigenvectors of C and
the ‘vector’ portion of the name will make more sense after you’ve studied vectors.
Okay, you should be mostly ready to start on your own. In the following exercises, you’ll be
using the matrix 123
G = 2 3 1...
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