{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MATH 330H 41 - Math 330 Homework 4.1(Pages 223,224 For...

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

View Full Document Right Arrow Icon
Math 330 Homework 4.1 (Pages 223,224) For problems (6) and (8) decide if the set is a subspace of P n for an appropriate value of n . Justify your answer. (6) All polynomials of the form p ( t ) = a + t 2 where a R . SOLUTION: This is not a vector space since the sum of two polynomials of this form is never of this form. For example, although 1 + t 2 belongs to this collection, (1 + t 2 ) + (1 + t 2 ) = 2 + 2 t 2 does not. (8) All polynomials in P n such that p (0) = 0 . SOLUTION: This is a vector space. Suppose that p and q are both polynomials and p (0) = q (0) = 0. Then ( p + q )(0) = p (0) + q (0) = 0 + 0 = 0. Suppose further, that λ is any real number. Then ( λp )(0) = λ ( p (0)) = λ · 0 = 0. Therefore, scalar multiplication and addition preserves the criteria to be in this collection so this collection is indeed a vector space. In problems 16 and 18, let W be the set of all vectors of the form shown where a, b , and c represent arbitrary real numbers. Either find a set of vectors which spans W or explain why W is not a vector space. (16) - a + 1 a - 6 b 2 b + a SOLUTION: This is not a vector space. Notice that although the following two matrices separately satisfy
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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