Answer:
Goodluck my dude.
Step-by-step explanation:
Answer:
Growth
Step-by-step explanation:
Answer with Step-by-step explanation:
Given

A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is

. We have

so this vector field is not conservative.
- - -
Another way of determining the same result: We want to find a scalar function

such that its gradient is equal to the given vector field,

:

For this to happen, we need to satisfy

From the first equation, integrating with respect to

yields

Note that

*must* be a function of

only.
Now differentiate with respect to

and we have

but this contradicts the assumption that

is independent of

. So, the scalar potential function does not exist, and therefore the vector field is not conservative.
AX = B
1 -1 -1 x 0
0 -2 -1 y = -2
2 1 0 z -4
x
y = A^-1 B
z
x -1 1 1 0 6
y = 2 -2 -1 . 2 = -8
z -4 3 2 4 14