{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Fall 2005 - Wickramasekera's Class - Practice Exam 1

# Fall 2005 - Wickramasekera's Class - Practice Exam 1 - MATH...

This preview shows pages 1–3. Sign up to view the full content.

MATH 20F: LINEAR ALGEBRA, WINTER 2007 MIDTERM 1 PRACTICE PROBLEMS Note: This is not a practice exam; you don’t have to be able to do these problems all in 50 minutes. Some of these problems are longer than any of the problems on the actual exam. (1) Find the solution(s) to the following system of linear equations by row reducing the associated augmented matrix. If the system has more than one solution, express the set of solutions in parametric vector form. x 1 - x 2 + 2 x 3 - x 4 = - 1 2 x 1 + x 2 - 2 x 3 - 2 x 4 = - 2 - x 1 + 2 x 2 - 4 x 3 + x 4 = 1 3 x 1 - 3 x 4 = - 3 (2) For which value(s) of a does the following system have zero, one, in- finitely many solutions? x 1 + 2 x 2 - 3 x 3 = 4 3 x 1 - x 2 + 5 x 3 = 2 4 x 1 + x 2 + ( a 2 - 14) x 3 = a + 2 (3) Determine whether the following set of vectors in R 3 is linearly inde- pendent. { (2 , - 1 , 4) , (3 , 6 , 2) , (2 , 10 , - 4) } . (Note that here we have used the al- ternate notation of writing vectors as rows rather than as columns.) 1

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

View Full Document
(4) Let u , v and w be any three vectors in R n . Prove that the vectors u - v , v - w and w - u form a linearly dependent set.
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