A when b is obtained from a by replacing row five

Info icon This preview shows pages 4–5. Sign up to view the full content.

View Full Document Right Arrow Icon
(a) When B is obtained from A by replacing row five with negative twenty-nine times row three plus row five, then det(B) = . (b) When C = A 5 , det(C) = . (c) If D is obtained from A by interchanging rows three and five, then det(D) = . (d) If E is obtained from A by replacing row four with negative two times row four, then det(E) = . (e) What can you say about the kernel of the linear transformation T: 6 6 defined by T( x ) = A x ? Why??
Image of page 4

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

View Full Document Right Arrow Icon
MidTest/MAS3105 Page 5 of 5 6. (10 pts.) Obtain an LU factorization for the matrix A below. 1 -2 1 -4 A = 3 -6 0 0 -6 12 -3 12 7. (10 pts.) Suppose that the matrix A has the following LU factorization: 1 0 0 3 -1 4 -8 A = -7 1 0 0 -7 2 15 3 25 1 0 0 1 -4 . (a) If b is an element of 3 , the problem of solving the equation A x = b may be handled by solving a pair of matrix equations in a particular order. Give the equations, complete with their coefficient matrices, in the correct order. Use all of the information at hand, but do not attempt to solve either equation. (b) Do the columns of A span 3 ? How do you know?? (c) Are the columns of A linearly independent? How do you know??
Image of page 5
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