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2331_Notes_6o1_fill - Math 2331 Linear Algebra Section 6.1...

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Math 2331 Linear Algebra Section 6.1 Eigenvalues and Eigenvectors Consider a function . What do the elements in the domain look like? ( ) : n f x \ \ n What do the elements in the range look like? So, we can think of any vector x as the input to a function and Ax as the output. What does Ax do to a vector? Example: Let 1 2 0 1 A = and find Ax for the following vectors 0 1 x = 1 1 x ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ 1 3 x = 1 3 x = 1 0 x =
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What is special about the last one? Another Example - 1 4 2 3 A = Find Ax when x is- 0 1 x = 1 0 x = 1 1 x ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ 2 1 x = The fact that the function f(x) = Ax does not change the direction of certain vectors is very significant.
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