sampleexam1 - 0 5-2 8 4-1 3-6 1-2 1 0 5-2 8 0 7-1-6 4...

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

View Full Document Right Arrow Icon
MAS 3114, Fall 10, Exam 1 No Calculators, books, or notes. 1. True/False: Mark each of the following as either True or False. No explanation required. 1. In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. 2. An inconsistent system has more than one solution. 3. When u, v R 3 are non-zero vector, Span( { u, v } ) contains the line through u and the origin. 4. The equation Ax = b is consistent if the augmented matrix [ A | b ] has a pivot position in every row. 5. Elementary row operations on an augmented matrix never change the solution set of the associated linear system. 2. Find h and k so that the system with augment matrix 1 3 2 5 h k has (a) no solution; (b) many solutions. 3. Find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first. 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
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 0 5-2 8 4-1 3-6 , 1-2 1 0 5-2 8 0 7-1-6 . 4. Suppose the augmented matrix [ A | u ] is row equivalent to B = 1 0 0 2 0 1 0 3 0 0 1 5 0 0 0 0 . 1 • Is u in the span of the columns of A ? • Do the columns of A span R 4 ? 5. Suppose C is row equivalent to D = 1 1 0 0 0 0 0 1 2 0 0 0 0 0 1 • Do the columns of C span R 3 ? • Can every vector in R 3 be written as a linear combination of the columns of C ? 6. A mining company owns two mines. Mine 1 produces 20 tons of copper and .11 tons of silver per day; and mine 2 produces 30 tons of copper and .1 tons of silver per day. Let x j denote the number of days mine j operates. Write a system of equations whose solution gives the number of days each mine should operate to produce 150 tons of copper and .6 tons of silver. 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