Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate ∫ C F ⋅ d r . F ( x , y ) = x i + y j C : r ( t ) = ( 3 t + 1 ) i + t j , 0 ≤ t ≤ 1
Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate ∫ C F ⋅ d r . F ( x , y ) = x i + y j C : r ( t ) = ( 3 t + 1 ) i + t j , 0 ≤ t ≤ 1
Solution Summary: The author explains how to calculate the value of displaystyleundersetCintF.dr if F(x,y)=xst
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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.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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