Quiz 1 - Solutions - equation A x = b meaning b is not in...

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

View Full Document Right Arrow Icon
Math 54 Quiz 1 Mike Hartglass September 4, 2010 1.) (3 points) Solve the following system of equations x 1 - 3 x 3 = 8 2 x 1 + 2 x 2 + 9 x 3 = 7 x 2 + 5 x 3 = - 2 The corresponding augmented matrix is: 1 0 - 3 8 2 2 9 7 0 1 5 - 2 1 0 - 3 8 0 2 15 - 9 0 1 5 - 2 1 0 - 3 8 0 1 5 - 2 0 2 15 - 9 1 0 - 3 8 0 1 5 - 2 0 0 5 - 5 1 0 - 3 8 0 1 0 3 0 0 1 - 1 1 0 0 5 0 1 0 3 0 0 1 - 1 meaning x 1 = 5, x 2 = 3 and x 3 = - 1. 1
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 A = 1 4 - 2 - 1 1 3 0 5 1 and b = 0 0 1 . Is b in the span of the columns of A ? Explain. b is in the span of the columns of A if and only if A x = b has a solution. The corresponding augmented matrix for this system is: 1 4 - 2 0 - 1 1 3 0 0 5 1 1 1 4 - 2 0 0 5 1 0 0 5 1 1 1 4 - 2 0 0 5 1 0 0 0 0 1 . The last matrix is that of an inconsistent system, so there is no solution to the
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: equation A x = b meaning b is not in the span of the columns of A . 3.) The following augmented matrices represent systems of equations. For each case determine if there is one solution, infinitely many solutions or no solution. ± 1 0 2 0 0 4 ² No solutions 1 5 3 8 0 1 4 5 0 0 1 9 0 0 0 0 One solution 1 4 6 10 0 3 4 1 0 0 2 5 One solution ± 1 0 3 0 0 0 ² Infinitely many solutions 2...
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