By hand, determine the rank of the following matrices by transforming them to row echelon form (REF). Based on your calculations, are the row vectors linearly independent? If the rows are linearly dependent, determine by hand a non-trivial set of values for the scalars c_1 ellipsis c_m that would make c_1 R_1 + c_2 R_2 + ellipsis + c_m R_m = 0 (where R_1 is the row 1 vector, R_2 is the row 2 vector, etc.). a. A = [1 3 2 4] b. B = [1 4 7 2 5 8 3 6 9] c. C = [1 4 7 2 5 8 3 6 10] d. D = [3 1 -2 2 0 -2 -1 2 3 4 3 -1] Do your work by hand and then check it in MATLAB. Show your MATLAB work. Verify your results for matrices A, B, and C by using the determinant. Lastly, for each matrix, plot the columns as vectors on the same set of axes. Describe the span and linear independence of the column vectors. You may sketch your plots by hand or you may use MATLAB or any other software to make your plots (including the software at the links shown in the lecture notes)