A panicle moving in a planar force field has a position vector x that satisfies x′ = A x. The 2 × 2 matrix A has eigenvalues 4 and 2, with corresponding eigenvectors v 1 = [ − 3 1 ] and v 2 = [ − 1 1 ] . Find the position of the particle at time t , assuming that x (0) = [ − 6 1 ] .
A panicle moving in a planar force field has a position vector x that satisfies x′ = A x. The 2 × 2 matrix A has eigenvalues 4 and 2, with corresponding eigenvectors v 1 = [ − 3 1 ] and v 2 = [ − 1 1 ] . Find the position of the particle at time t , assuming that x (0) = [ − 6 1 ] .
A panicle moving in a planar force field has a position vector x that satisfies x′ = Ax. The 2 × 2 matrix A has eigenvalues 4 and 2, with corresponding eigenvectors v1 =
[
−
3
1
]
and v2 =
[
−
1
1
]
. Find the position of the particle at time t, assuming that x(0) =
[
−
6
1
]
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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