MTH 341 Study Guide - Final Guide: Thx, Solution Set

• School: Oregon State University
• Department: Mathematics
• Course: MTH 341
• Professor: Rockwell, Dan

Document Summary

Directions: discuss and solve the following problems in your groups. You are encouraged to write out your work on additional pieces of paper. (1) (a) find a basis for the null space of a (denoted null(a)) for the matrix below. 7 (b) how many free variables does the solution set for the equation a~x = ~0 have? (2) let. A very useful theorem from our book is often called the rank-nullity theorem. Let a be an (m n) matrix. Note: dim(null(a)) is often denoted nullity(a). (3) suppose the matrix a has 3 rows, rank(a) = 3, and the solution set to a~x = ~0 has. Justify your answer. (5) true or false: for all (m n) matrices a and b, nullity(a + b) = nullity(a)+ nullity(b). Page 3 of 3 (7) challenge problem: let a be any (n n) matrix.