homework set 15-A-Solutions

# homework set 15-A-Solutions - BILKENT UNIVERSITY Department...

This preview shows pages 1–2. Sign up to view the full content.

B ˙ ILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set 1 # 15-A U. Mu˘gan July 2, 2008 Homework problems from the 2 nd Edition, SECTION 4.6 4) Yes, the three vectors are mutually orthogonal, since ~v 1 .~v 2 = 3 + 4 + 9 - 12 - 4 = 0 , ~v 1 .~v 3 = 6 + 4 + - 12 - 2 + 4 = 0 , ~v 2 .~v 3 = 18 + 4 - 12 + 6 - 16 = 0 . 7) Let ~u = CB, ~v = CA and ~w = AB , then a = | ~u | , b = | ~v | and c = | ~w | so as to verify that a 2 + b 2 = c 2 . For given vectors a 2 = 19 , b 2 = 25 and c 2 = 44 . 17) Denote by A the matrix having the given vectors as its row vectors, and by E the reduced echelon form of A . From E we find the general solution of the homogeneous system A˜x = ˜ 0 in terms of parameters s, t, .... We then get basis vectors ~u 1 , ~u 2 , ... for the orthogonal complement V by setting each parameter in turn equal to 1 (and the others then equal to 0). The echelon form E of the given matrix A is E = 1 0 - 7 19 0 1 3 5 . x 1 = s, x 4 = t, x 2 = - 3 s + 5 t, x 1 = 7 s - 19 t. Therefore ~u 1 = (7 , - 3 , 1 , 10) , ~u 2 = ( - 19 , 5 , 0 , 1) .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern