MATH 461 Midterm: MATH461 BOYLE-M SUMMER I2006 0101 MID SOL 1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 461
• Professor: All

Document Summary

Math 461-0101 summer 2006 exam 2 solutions: (16 points) put the matrix. 0 8 2 4 6 into row echelon form. Then nd a basis for each of the following: (a) col(a), the column space of a. (b) nul(a), the null space of a. (c) row(a), the row space of a. First we apply elementary operations to put a into a row echelon form b: Now, columns two and four of b are pivot columns, and so columns two and four of a will be a basis for the column space of a. Rows one and two of b are a basis for row(a), since row(a) = row(b). For nul(a), we continue with elementary row operations to put b into the reduced row echelon form c: The columns 1,3,5 of c (or b) without a pivot correspond to free variables .