MATH 307 Midterm: MATH 307 2008 Winter Test 1

• School: UBC
• Department: Mathematics
• Course: MATH 307
• Professor: all

Document Summary

Do not open this test until instructed to do so! This exam should have 12 pages, including this cover sheet. No textbooks, calculators, or other aids are allowed. Turn o any call phones, pagers, etc. that could make noise during the exam. You must remain in this room until you have nished the exam. Use the back of the page if necessary. Determine the rank of a and nd a basis of the left null space n (a ) of a. Let p3 be the vector space of polynomials of degree 3. The monomials 1, x, x2, x3 form a basis of p3. Consider the linear mapping from p3 into p3 given by p(x) 7 p (x). Find the matrix a of the mapping with respect to the monomial basis and determine its null space. For the parameter , consider the linear system: x y + z = 2,