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Exercise 9. Let u = (1,2) and v = (2, 1). Find a nonzero linear combination i of u and v that's perpendicular to u. Draw a picture to illustrate what the coefficients are measuring. (Hint: you may as well take the linear combination ī to be of the form Au+v ; why is that? Then how would you find X?)

Exercise 9. Let u = (1,2) and v = (2, 1). Find a nonzero linear combination i of u and v that's perpendicular to u. Draw a picture to illustrate what the coefficients are measuring. (Hint: you may as well take the linear combination ī to be of the form Au+v ; why is that? Then how would you find X?)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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solve exercies 9 with explanation asap
Exercise 8. Let u = (1, 2). Find a nonzero vector v e R² perpendicular to u. Show how to express any vector (r, y) e R² as a linear combination of u and v. Illustrate by plotting u, v and (r, y) in the plane and indicate what the coefficients are measuring. Use some specific examples and moderately accurate pictures to verify. Exercise 9. Let u = (1, 2) and v = (2, 1). Find a nonzero linear combination i of u and v that's perpendicular to u. Draw a picture to illustrate what the coefficients are measuring. (Hint: you may as well take the linear combination ī to be of the form Au + v ; why is that? Then how would you find A?) Exercise 10. Write down the system of two linear equations in two unknowns to express (3, 5) as a linear combination of u = (1,2) and v = (2,1). Then solve that system and check that your solution solves the problem. Draw a picture to illustrate the solution.
Transcribed Image Text:Exercise 8. Let u = (1, 2). Find a nonzero vector v e R² perpendicular to u. Show how to express any vector (r, y) e R² as a linear combination of u and v. Illustrate by plotting u, v and (r, y) in the plane and indicate what the coefficients are measuring. Use some specific examples and moderately accurate pictures to verify. Exercise 9. Let u = (1, 2) and v = (2, 1). Find a nonzero linear combination i of u and v that's perpendicular to u. Draw a picture to illustrate what the coefficients are measuring. (Hint: you may as well take the linear combination ī to be of the form Au + v ; why is that? Then how would you find A?) Exercise 10. Write down the system of two linear equations in two unknowns to express (3, 5) as a linear combination of u = (1,2) and v = (2,1). Then solve that system and check that your solution solves the problem. Draw a picture to illustrate the solution.
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