practice-Math33A-mt1

practice-Math33A-mt1 - 1 1 1 Find a basis for S ⊥ 3 The...

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

View Full Document Right Arrow Icon
Name: Student ID: Section: 2 Prof. Alan J. Laub Apr. 25, 2008 Math 33A – MIDTERM EXAMINATION I Spring 2008 Instructions: (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. (b) Notation will conform as closely as possible to the standard notation used in the lectures. (c) Do all 4 problems. Each problem is worth 25 points. Some partial credit may be assigned if warranted. (d) Label clearly the problem number and the material you wish to be graded. 1. You are given the matrix A = 1 2 0 4 1 0 1 0 2 1 0 0 0 0 2 IR 3 × 5 . (a) Put A in row-reduced echelon form (rref). (b) Find a basis for Im( A ) from rref( A ). (c) Find a basis for Ker( A ) from rref( A ). (d) What is rank( A )? What is rank( A T )?
Image of page 1

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

View Full Document Right Arrow Icon
2. Let S = Sp 1 1 1
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 1 1 . Find a basis for S ⊥ . 3. The vector •-4 7 ‚ has components 5 and-3 with respect to the basis ‰• 1 2 ‚ , • 3 1 ‚± . What are the components of the vector •-4 7 ‚ with respect to the basis ‰• 1 ‚ , • 1-1 ‚± of IR 2 ? 4. (a) Suppose A ∈ IR 19 × 48 8 , i.e., A is the coefficient matrix of a system of 19 equations in 48 unknowns but only 8 of the equations are independent. How many linearly independent solutions can be found to the homogeneous linear system Ax = 0? (b) For the same A as in (a), how many linear independent solutions can be found to the homogeneous linear system A T y = 0?...
View Full 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