README to accompany the m-files dispsysmat.m interchangedisp.m replacedisp.m scaledisp.m interchange.m replace.m scale.m gauss.m bgauss.m transUH.m plotaxes.m plotvector.m plotbasisgrid.m for use with Math2331, Fall 2013. INSTALL: Place in the Matlab folder or in the folder in which you install Octave. To find out where you should put the m-files, start Matlab or Octave and type the command pwd (print working directory) which returns a path to the currently active directory/folder. This is where you should put the m-files. USE: Now you can create matrices, view the corresponding systems and perform elementary row operations. EXAMPLES: A=[2 4 3 1; 1 0 1 3; 0 2 2 2]; creates the augmented matrix -- -- | 2.000000 4.000000 3.000000 1.000000 | | 1.000000 0.000000 1.000000 3.000000 | | 0.000000 2.000000 2.000000 2.000000 | -- -- belonging to the linear system 2.000000 x_1 + 4.000000 x_2 + 3.000000 x_3 = 1.000000 1.000000 x_1 + 0.000000 x_2 + 1.000000 x_3 = 3.000000 0.000000 x_1 + 2.000000 x_2 + 2.000000 x_3 = 2.000000 Aprime=interchangedisp(A,row1,row2); interchanges row1 and row2 in the augmented matrix A, displays the new system and corresponding augmented matrix and stores the result in the augmented matrix Aprime Aprime=scaledisp(A,row,multiple); scales row in the augmented matrix A, displays the new system and corresponding augmented matrix and stores the result in the augmented matrix A prime Aprime=replacedisp(A,row1,row2,multiple); replaces row1 in the augmented matrix A by the sum of row1 and row2 times multiple, displays the new system and corresponsing augmented matrix and stores the result in the augmented matrix Aprime Aprime=interchange(A,row1,row2) interchanges row1 and row2 in the augmented matrix A, returns the new augmented matrix Aprime=scale(A,row,multiple) scales row of matrix A by multiple, returns new augmented matrix Aprime=replace(A,row1,row2,multiple) replaces row1 in the augmented matrix A by the sum of row1 and row2 times multiple, returns new augmented matrix Aprime=gauss(A, row) finds the leading non-zero entry in a row, creates zeros in the column below this leading entry by elemtary row operations Aprime=bgauss(A,row) finds the leading non-zero entry in a row, creates zeros in the column above this leading entry by elementary row operations B=transUH(A); takes as its input a 2x2 matrix A, plots a polygonal path in the shape of UH, then plots the images of the vectors on this path under the transform given by the matrix A plotaxes([xmin xmax ymin ymax]); plots a coordinate system with a range for x-values from xmin to xmax and a range for y-values of yin to ymax plotvector([x; y], width); if plotaxes has been used before, then plotvector plots a vector with entries x and y as an arrow with a tip of given width plotbasisgrid(P_B); if plotaxes has been used before, then plotbasisgrid plots the two basis vectors given by the columns of P_B in arrow form and plots the points corresponding to integer linear combinations of the basis vectors with coefficients ranging from -2 to 2