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**Unformatted text preview: **ors in R2 and maps them to vectors in R2 . This function is an example of something we’ll
call a linear map.
We can look at speciﬁc vectors like
(8) L 1
0 = 2 0
0 3 1
0 = 2
0 , (9) L 0
1 = 2 0
0 3 0
1 = 0
3 , L 1
1 = 2 0
0 3 1
1 = 2
3 . and
(10) If you draw the vectors and what they map to, you’ll see that the unit square is being mapped to a rectangle
1
0
stretched by a factor of 2 in the
direction and by a factor of 3 in the
direction.
0
1
1 MA 3280 Lecture 23 - More on Eigenvectors 2 Something similar is happening in the linear map
(11) x1
x2 L 1 −1
2
4 = x1
x2 = x1 − x2
2x1 + 4x2 , although it’s probably not as clear. Note that the matrix is the same one that we found eigenvalues and
eigenvectors for. The eigenvectors map as follows.
L 1
−1 = 1 −1
2
4 1
−1 = 2
−2 L (12) 1
−2 = 1 −1
2
4 1
−2 = 3
−6 and
(13) Here, the mapping stretches by...

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