This exercise concentrates on the row-reduced echelon form of matrices. Matrices A1 and A2 have been stored in a file called HW3.MAT. Begin by loading the matrices into memory from the disk (choose the Disk Operations menu).
1. Go first to the "Reduced Echelon Form" program by selecting "Other Operations" from the Matrix Operations menu, then selecting "Reduced Echelon Form" from the submenu. Select the matrix A1, and, when its reduced echelon form has been calculated, keep it as Ech1 and have it printed.
2. Now go back to the menu and select "Row Operations". Select the same matrix A1 and try applying row operations to obtain its row echelon form via Gauss-Jordan Elimination (text, p. 61). What happens? Can you guess why? Print the result.
3. Choose A1 again in "Row Operations". Do 5 randomly chosen row operations on A1 (using scalars of reasonable sizes) to produce a matrix which you keep under the name A3. Then go to "Reduced Echelon Form" and apply it to A3, keeping and printing the result as Ech3. Compare Ech3 and Ech1. What has happened and why?
4. Get the row echelon form (as above) of A2, keep and print it as Ech2. Get the sum of A1 and A2 (using "Sum" in the Matrix Operations menu), keep it as A4 and then get the reduced echelon form of A4. Do you see any relation between the result and Ech1 + Ech2, or A1 + A2? Should there be any?
Hand in the results, with your conclusions (they are allowed to be tentative).
