- Problem 4 3 Points Throughout This Question You Are Required To Work In Mod 2 Arithmetic I E The Field F 0 1 1 (56.48 KiB) Viewed 22 times
Problem 4. (3 points) Throughout this
question you are required to work in mod 2 arithmetic, i.e., the field F₂ = {0, 1}. Consider the two matrices A and B The MATLAB code to produce A and B is given by: A = [0,1,1,1,0;0,0,1,0,0] B = [1,0,0,0; 1,0,0,1;0,0,1,1,1,0,0,0,1,1,1,0] (a) Find A B using mod 2 arithmetic. (b) Select the columns, if any, in B that give vectors in the null space of A using mod 2 arithmetic. If none, select "None of the above". A. Column 1 B. Column 2 C. Column 3 D. Column 4 E. None of the above A = AB= 0 1 € M2,5(F₂) 0 [1 0 0 0 0 0 1 0 1 1 € M5,4 (F₂) 0 0 1 0 0 1 B 0 1 1 0 10 0 10 11
(c) Select all of the following vectors that are in the row space of A using mod 2 arithmetic. If none, select "None of the above". A. (0, 0, 1, 0, 0) B. (0, 1, 1, 0, 0) C. (0, 1, 0, 1, 0) D. (1, 0, 0, 0, 1) E. (1, 0, 0, 0, 0) F. (0, 0, 0, 0, 0) G. None of the above