Pick two random looking and linearly indepen try to find a vector w which is orthogonal to bo explore how to find all possible vectors w using a system of linear equations using the entries variables; solve this system of equations to find v. Check that u w = 0 and vw= = 0 by hand. 1. How many equations did you need to solve
Pick two random looking and linearly indepen try to find a vector w which is orthogonal to bo explore how to find all possible vectors w using a system of linear equations using the entries variables; solve this system of equations to find v. Check that u w = 0 and vw= = 0 by hand. 1. How many equations did you need to solve
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
![Pick two random looking and linearly independent vectors u and v in R" with n ≥ 4, and
try to find a vector w which is orthogonal to both u and v by guess-and-check. Next, we will
explore how to find all possible vectors w using systems of equations. To that end, write down
a system of linear equations using the entries of u, v as coefficients and the entries of w as
variables; solve this system of equations to find w such that w is perpendicular to both u and
v. Check that u w = 0 and vw = 0 by hand.
1. How many equations did you need to solve in order to find w? and how many variables?
2. Why is any vector in Col([u v]) perpendicular to w?
3. Why is a vector in Nul([u v]T) orthogonal to both u and v?
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1c8b225-0b34-4b80-be8e-a744772fc824%2F03a63112-0ca9-473b-865a-8afff567530d%2Ftcvkz59_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Pick two random looking and linearly independent vectors u and v in R" with n ≥ 4, and
try to find a vector w which is orthogonal to both u and v by guess-and-check. Next, we will
explore how to find all possible vectors w using systems of equations. To that end, write down
a system of linear equations using the entries of u, v as coefficients and the entries of w as
variables; solve this system of equations to find w such that w is perpendicular to both u and
v. Check that u w = 0 and vw = 0 by hand.
1. How many equations did you need to solve in order to find w? and how many variables?
2. Why is any vector in Col([u v]) perpendicular to w?
3. Why is a vector in Nul([u v]T) orthogonal to both u and v?
10
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