MATH 0520 Midterm: MATH 052 Brown Midterm2sol

• School: Brown University
• Department: Mathematics
• Course: MATH 0520
• Professor: All

Document Summary

Suppose that a is a 3 3 matrix with the property that av1 = e1, av2 = e2, and av3 = e2 + e3, where v1 = . Find a 1. (note: e1e2, e3 denote the standard basis vectors in r3. ) Suppose t is a real number and a = t. Show that det( a + b) is not always equal to det( a) + det(b), where a and b are 2 2 matrices. Hint: just make up some examples for a and b; it will probably work. Find a basis for the row space of a and a basis for the column space of a. Final answer: now space , the pilot columns of t form. Find the rank and the nullity of a. Consider the set s = { f c([0, 1]) : f (x) 0 for all x [0, 1]} of continuous functions from [0, 1] to r which are nowhere negative.