ū = the vector starting at the point (2,4) and ending at the point (5, 11), ✓ = the vector starting at the point (2,4) and ending at the point (-4, 5). For this part include a graph of the points, vectors, and parallelogram.
ū = the vector starting at the point (2,4) and ending at the point (5, 11), ✓ = the vector starting at the point (2,4) and ending at the point (-4, 5). For this part include a graph of the points, vectors, and parallelogram.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Part D please
![Area Theorem:
If A is a 2 x 2 matrix, the area of the parallelogram determined by the columns of A is the
absolute value of the determinant of A, Area = |det (A)]. The same formula calculates the
volume of the parallelepiped determined by the columns of A, if A is a 3 x 3 matrix.
Example: The vectors u = (2, 1), ✓ = (3,0) define the parallelogram
-1
0
u
A
V
=
2
=[²3], det A
=
3
-3, [det(A)| = |−3| = 3
5
Exercise Set 1:
Write the matrix A from the given vectors. Calculate the area (or volume) of the parallelogram
(parallelepiped) defined by them.
(a) u = (1,4), v = (5,0)
(b) u = (3,2), v = (6,−4)
(c) ū = (2,5,0), v = (3,−2,−1), w = (−1,4, 3)
(d) u = the vector starting at the point (2, 4) and ending at the point (5, 11),
✓ = the vector starting at the point (2, 4) and ending at the point (-4, 5).
For this part include a graph of the points, vectors, and parallelogram.
Note that the above Area Theorem can be generalized to what is called the Shoelace Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eeaacd3-f9c7-4223-a8e6-a717e551a98a%2F8084a412-a85b-49f9-aa9a-0bfd4bf3e2c6%2Fy9klj18_processed.png&w=3840&q=75)
Transcribed Image Text:Area Theorem:
If A is a 2 x 2 matrix, the area of the parallelogram determined by the columns of A is the
absolute value of the determinant of A, Area = |det (A)]. The same formula calculates the
volume of the parallelepiped determined by the columns of A, if A is a 3 x 3 matrix.
Example: The vectors u = (2, 1), ✓ = (3,0) define the parallelogram
-1
0
u
A
V
=
2
=[²3], det A
=
3
-3, [det(A)| = |−3| = 3
5
Exercise Set 1:
Write the matrix A from the given vectors. Calculate the area (or volume) of the parallelogram
(parallelepiped) defined by them.
(a) u = (1,4), v = (5,0)
(b) u = (3,2), v = (6,−4)
(c) ū = (2,5,0), v = (3,−2,−1), w = (−1,4, 3)
(d) u = the vector starting at the point (2, 4) and ending at the point (5, 11),
✓ = the vector starting at the point (2, 4) and ending at the point (-4, 5).
For this part include a graph of the points, vectors, and parallelogram.
Note that the above Area Theorem can be generalized to what is called the Shoelace Theorem.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
