MATH 337 Final: MATH 337 NJIT Math337prac Final f2011

• School: New Jersey Institute of Technology
• Department: Mathematical Sciences
• Course: MATH 337
• Professor: All

Document Summary

Math 337 _ final exam _ fall 2011. Show all work a. nd justify all steps of each argument you make. 1 ) ( 2 0 p o i n t s ) l e t a : (3,8,7)", ua : (5,12, 13)", and b : (b1,b2,fu)t . Find bases and dimensions of nul(a), col(a) and row(a). What is the rank of a? d)(5 points extra credit) find a basis for (row(a))l. 4 ) ( 2 0 ) l e t a : ( 3 , - 3 , 3 ) r . Express r in terms of q and a, but don"t compute it: (20 points) a) find the matrix a corresponding to the quadratic form q(o) : 3r7 + rhpz +3n2: is q positive definite, negative definite, or indefinite, orthogonally diagonalize a.