MATH 461 Final: MATH461 BOYLE-M SPRING2006 0101 FINAL SOL

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

Document Summary

Math 461-01** spring 2006 final exam. Solutions: (24 pts) let t be the linear transformation from r4 to r3 de ned as t (x) = ax, where. 8 (a) compute the reduced row echelon form of a. The reduced row echelon form is the matrix r obtained by elementary row opera- tions from a as follows: = r . (b) find a basis for the kernel of t . One basis is given by the two column vectors [ 5, 3/2, 0, 1]t and [ 6, 5/2, 1, 0]t . (c) find a basis for the range (i. e. , the image) of t . The rst two columns of a are one such basis. (d) find a basis for the row space of a. The rst two rows of r are one such basis: (16 pts) for x = (x1, x2) in r2, let q(x) = (x1)2 + 4x1x2 + 3(x2)2. Determine whether the quadratic form q(x) is positive de nite.