In Problem 13-19 , determine whether the given vector functions are linearly dependent ( L D ) or linearly independent ( L I ) on the interval ( − ∞ , ∞ ) . 19 . [ 1 0 1 ] , [ t 0 t ] , [ t 2 0 t 2 ]
In Problem 13-19 , determine whether the given vector functions are linearly dependent ( L D ) or linearly independent ( L I ) on the interval ( − ∞ , ∞ ) . 19 . [ 1 0 1 ] , [ t 0 t ] , [ t 2 0 t 2 ]
Solution Summary: The author explains that the given vector functions are linearly dependent or independent on the interval (-infty,
In Problem 13-19, determine whether the given vector functions are linearly dependent
(
L
D
)
or linearly independent
(
L
I
)
on the interval
(
−
∞
,
∞
)
.
19.
[
1
0
1
]
,
[
t
0
t
]
,
[
t
2
0
t
2
]
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
If x2 +y2+z2 = 9,dx/dt =5 , and dy/dt =4, find dz/dtwhen (x,y,z) =(2, 2,1).
Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P (1, 1), in which z = 1. The value of the directional derivative of z at P in the direction of the vector w = (1, −1), corresponds to:
Chapter 9 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
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