Math 2641 (Fall 2022) Homework Set #09 (Due 11/11) Problems 2 4 2 4 2 Problem 9.1. Let. A = 5 10 4 12 3 , which is a. 3 x 5 matrix. 3 6 5 2 4 (1) Find a basis for Col/1. (2) Find a basis for NulA. 2 4 2 4 2 Problem 9.2. Let. A : 5 10 4 12 3 be as in Problem 9.1 3 6 5 2 4 (1) Find dim(Col A), dim(RowA), and rank A. (2) Find dim(NulA). (3) Calculate rankA + dim(NulA). 2 4 6 8 easy to verify) that. both 8 2 {b1, b2} and C 2 {01, C2} are ordered/ indexed bases of R2. P 13: Problem 9.3. Let. b1 : [1], b2 : [3], c1 : l7], and c2 : [11] in R2. It. is known (and (1) Determine C the change-ofcoordinates matrix from B to C. (2) Determine Bi, the changeofcoordinates matrix from C to 8. Problem 9.4. Let b1 : ['21]: b2 : [i]: (:1 : [g] (:2 : [181), B : {[31, b2} and C 2 {ch C2} be as in Problem 9.3. ( 1) If u E R2 satises [Ills = [:1], express [tile in terms of 11.1 and 1:2. 2 \"U 1 1,2 (2) If v E R2 satises [v]C = l :| , express [v];; in terms of 1:1 and \"02