In Problems 13-19 , determine whether the given vector functions are linearly dependent ( L D ) or linearly independent ( L I ) on the interval ( − ∞ , ∞ ) . [ t 3 ] , [ 4 1 ]
In Problems 13-19 , determine whether the given vector functions are linearly dependent ( L D ) or linearly independent ( L I ) on the interval ( − ∞ , ∞ ) . [ t 3 ] , [ 4 1 ]
Solution Summary: The author explains how Wronskian's n vector functions are linearly independent on the interval (-infty), if the determinant is non-zero, then the vector
In Problems 13-19, determine whether the given vector functions are linearly dependent
(
L
D
)
or linearly independent
(
L
I
)
on the interval
(
−
∞
,
∞
)
.
[
t
3
]
,
[
4
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.
In problem2 , find a vector in whose direction f(x,y,z) has zero change (zero derivative) at point (2,1,-1)
Problem 2 - Find the directional derivative of f(x,y,z)=4x^2y-7z^3x+y^2 at the point (2,1,-1) in the direction of vector v=3i-2j+5k
Solve the initial value problems for r as a vector function of t:
10.Suppose that each of the vectors x(1), …, x(m) has n components, where n < m. Show that x(1), …, x(m) are linearly dependent.
In each of Problems 11 and 12, determine whether the members of the given set of vectors are linearly independent for −∞ < t < ∞ . If they are linearly dependent, find the linear relation among them.
Chapter 9 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
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