N 1 1 t 1 1 t o select from the following 1 only d 2

Info icon This preview shows pages 7–8. Sign up to view the full content.

View Full Document Right Arrow Icon
n 1 1 T , 1 - 1 T o Select from the following: 1. Only D. 2. Only C. 3. Only B. 4. Only A. 5. None of the above. Answer: 2 The null space is given by a b c R 3 : 0 1 - 1 0 - 1 1 a b c = 0 0 = a b c R 3 : b - c b - c = 0 0 = a b c R 3 : b = c = a b b R 3 = a 1 0 0 + b 0 1 1 : a, b R = span 1 0 0 , 0 1 1 . 7
Image of page 7

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

View Full Document Right Arrow Icon
Since 1 0 0 , 0 1 1 is a linearly independent set, we have a basis for the null space. Thus every basis must have two elements which are column vectors in R 3 . We need only consider B and C. Since 1 0 0 / span n 0 1 - 1 T , 0 - 1 1 T o B does not span the null space and is not a basis for the null space. The set in C is linearly independent and span n 1 1 1 T , 0 1 1 T o = a a + b a + b R 3 : a, b R = α β β R 3 : α, β R by relabeling α = a and β = a + b (note that β can take on any real value independently of α ). Thus C provides a basis for the null space.
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern