The dot product of vectors can be used in business applications. For Exercises 87-88, find the dot product and interpret the results. The components of n = 500 , 330 represent the number of T-shirts and hats, respectively, in the inventory of a surf shop. The components of p = 15 , 9 represent the price (in $) per T-shirt and hat, respectively. Find n ⋅ p and interpret the result.
The dot product of vectors can be used in business applications. For Exercises 87-88, find the dot product and interpret the results. The components of n = 500 , 330 represent the number of T-shirts and hats, respectively, in the inventory of a surf shop. The components of p = 15 , 9 represent the price (in $) per T-shirt and hat, respectively. Find n ⋅ p and interpret the result.
Solution Summary: The author calculates the dot product ncdot p, which represents the total amount of money, if the entire inventory were sold.
The dot product of vectors can be used in business applications. For Exercises 87-88, find the dot product and interpret the results.
The components of
n
=
500
,
330
represent the number of T-shirts and hats, respectively, in the inventory of a surf shop. The components of
p
=
15
,
9
represent the price (in $) per T-shirt and hat, respectively. Find
n
⋅
p
and interpret the result.
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.
University Calculus: Early Transcendentals (4th Edition)
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