Let's try some elementary row operations to see how they work. Evaluate the following code:
A = Matrix(QQ, [[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print("Matrix A:")
show(A)
# Elementary row operations
print("Scaling second row by two:")
A.rescale_row(1, 2)
show(A)
print("Swapping first and second rows:")
A.swap_rows(0, 1)
show(A)
print("Adding 3*(row 1) to row 0:")
A.add_multiple_of_row(0, 1 ,3)
show(A)
print("A in echelon form:")
show(A.echelon_form())The result will look like this:
