%% Math 230 - Honors Introductory Linear Algebra %% MATLAB commands typed in Class on Tuesday, Feb 1, 2011 %% Lines that start with a '%' are comments - MATLAB ignores them %% (i.e., does not "execute" or "run" them as commands). % Exchange matrix for Prob 4, Page 63 A = [.65 .3 .3 .2 .1 .1 .15 .1 .25 .35 .15 .3 0 .25 .4 .4] size(A) A(1,2) % gives the entry in the first row and second column % In general, to access (i,j)-th element, we give A(i,j) A(1,:) % gives the first row, i.e., all elements in the first row A(:,3) % gives the 3rd column A(1,1)-1 % subtract 1 from the (1,1) entry of A, and just print the result out % without updating A(1,1) A(1,1)=A(1,1)-1 % subtract 1 from the (1,1) entry of A, updating A(1,1) to the new value A(1,1)=A(1,1)+1 % just going back to the original A(1,1) entry Acopy = A; % Creating a copy of A for future reference. % semicolon at end suppresses printing of the output % We need to do A(i,i) = A(i,i)-1 for i=1,2,3,4 1:4 % gives the numbers 1,2,3,4 % We use a "for" loop to do these repeated calculations for i=1:4 A(i,i) = A(i,i) - 1; end A Arref = rref(A) % reduced row echelon form of A % But let's do some of the EROs ourselves % % Scale R1 by (1/-0.35) so that A(1,1) becomes 1 A(1,:)*(1/-0.35) A(1,:) = A(1,:)*(1/-0.35) % The second command above reassigns A(1,:). % The replacement ERO R2-0.1xR1 (to zero out the entry in the (2,1)-position) A(2,:) = A(2,:) - 0.1*A(1,:) % swap R2 and R3 % we need to copy one of them to a temporary variable, and then effect the swap r = A(2,:) % second row is stored in r A(2,:) = A(3,:); A(3,:) = r % Now R2 and R3 are swapped