MATH 304 Midterm: MATH 304 Binghamton Exam2 Quincy Loney Practice Questions Solutions

• School: Binghamton University
• Department: Mathematical Science
• Course: MATH 304
• Professor: All

Document Summary

Exam 2 practice questions suggested by quincy loney: suppose a is a 4 3 matrix and b is a vector in r4 with the property that ax = b has a unique solution. Solution: the rref for a must have a pivot in the rst 3 rows followed by a zero row. If there were less than 3 pivots, there would be in nitely many solutions. The matrix a has 5 columns and 2 pivots. Hence there are 3 free variables. (note that one free variable is su cient for an a rmative answer. ) (b) yes. The matrix [a|b] has 2 rows and 2 pivots. There is no way to obtain a pivot in the augmented row: for the given matrices, nd a nonzero vector in nul(a) and a nonzero vector in col(a). (a) (b) . The null space of a matrix a is the set of all solutions of the homogeneous equation ax = 0.