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Unformatted text preview: is
parallel to the position
vector.
• That is, Av = λv. Introduction to systems of equations
• You should see two
“special” directions.
• What are they?
• Directions along which
the velocity vector is
parallel to the position
vector. Av = λv.
√
λ2 = − 2
√
1− 2
v2 =
1 • That is, Matrix review (eigencalculations)
• Find eigenvalues and eigenvectors of A= 1
4
1
.
1 Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv. Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv.
• What are the eigenvalues of A?
(A) 1 and 3
(B) 1 and 3
(C) 1 and 3
(D) 1 and 3
(E) Explain, please. Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv.
• What are the eigenvalues of A?
(A) 1 and 3
(B) 1 and 3
(C) 1 and 3
(D) 1 and 3
(E) Explain, please. Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv. Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv.
Av − λ v = 0 Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv.
Av − λ v = 0 (A − λI )v = 0 Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv.
Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0 Matrix review (eigencalculations)
11
• Find eigenvalues and eigenvectors of A =
.
41
• Looking for values λ and vectors v for which Av = λv.
Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0
1−λ
1
det
=0
4
1−λ Matrix review (eigencalculations)
11...
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This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.
 Spring '13
 EricCytrynbaum
 Differential Equations, Systems Of Equations, Eigenvectors, Equations, Vectors

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